Well, extrapolating from chimpanzees and dolphins, the results might be rather grim.
Males and females have contradictory goals in species where multiple mates are an option. The reproductive expenditure in males is minimal compared to the huge expenditure of females. Therefore they follow contradictory strategies. Males use a quantity over quality strategy while females use quality over quantity. Males will knock up any female but females will be selective.
Males can fertilize many females but they can't ever be sure which females carry their young unless they control access to the females during estrous and usually always. But the females don't necessarily view any particular mate as the optimum mate so they try to escape mating restriction. The males respond by forming alliance with other males to control the females, especially in their narrow reproductive windows.
Since the only reason for males to join an alliance is to improve their chances of passing on their genes, males have little to no incentive to form alliance with any other than close blood kin. That way, regardless of who succeeds in impregnating females, some of their genes get passed on.
The base social unit chimpanzees and dolphins is a group of males who are father, sons, brothers, nephews, cousins to each other. They spend most of their time capturing females, corralling them and fighting other male groups to steal their females. In general, they kill any non-related male they come across especially infants and juveniles.
Human societies eerily follow genetically optimal paths even though they have no concept of genetics or evolutionary theory. For example, in many small scale cultures, sexual fidelity of women in marriage is not strictly enforced and marriages are usually temporary. That means that no man can ever know child of his wife of the moment is his or not. In every known instance of such societies, men concentrate their paternal attention on their nephews and nieces born of their sisters. That way, at least some of their effort is guaranteed to go towards their own gene line.
Therefore, it's likely that human society with chimpanzee like mating conditions would adopt a chimpanzee like social structure. The base social unit would be a group of related men.
It's important to note that just because men could only mate episodically does not mean that their reproductive goals would not dominate their lives. Species devote time to reproduction based on the payoff off of reproductive success not how often they actually mate.
Men would attempt to control as large a group of women as possible at all times. With human technology, men could much more easily physically control women compared to chimpanzees or dolphins having to control females with just the males own bodies. Women would likely be treated as chattel.
Close personal relationships between men and women would be rare. Men would tend to view all women of reproductive age as interchangeable. Women would attempt to be more selective but the men would not allow them to do so. Since selectivity and romance might lead to jealousy and lethal conflict, the Men's moral culture might actively view selectivity, romance and even love as immoral and dangerous perversions.
"Marriages" would likely be one group of men sending their daughters out to close but not to closely related group of men for the purposes of forming military and economic alliances. New family groups of males would arise from multiple births to traded daughters from the same male group. Males would always stay with their families but women would get sent out although possibly in batches.
Close inbreeding would be a constant problem. Overall genetic diversity would be low. Entire male family groups could be wiped out by single disease.
When women came into estrous, they would be especially isolated or controlled not only to control access but to prevent violent quarrels among men. A detached woman with no controlling male group would be regarded as source of violent conflict and therefore very dangerous. A detached woman in estrous might be killed on sight just to prevent open war.
Since their sexuality only turned on episodically, men and women would emotionally bond with members of their own sex and would like socialize only within their own sex. Each sex would have it's own distinctive subculture.
The male society would likely be structured and hierarchical with great emphasis on ritual, respect and likely dueling. Males would mostly fight or train to do so. They would shun productive labor and see warrior as the ideal male. For the higher status males, they would rather starve than get their hands dirty.
Women's culture would likely be less hierarchical, would be based on status linked to age and number of sons. Since men would view women as interchangeable, women would not have status based on their mates rank or favoritism from males. Instead, status would likely depend on skill of assisting in child birth and general raising of children.
Boys would have to be raised by women at least to weaning age. In a bronze age culture that would be around 4. In known cultures where boys and girls are separated, the usual age is 7. Women will try to favor their own offspring so women will nurse and raise their own sons as much as possible. Therefore, a man's mother might be the only women he views as special and with affection. He might visit her and care for her specially.
A women's ultimate status therefore will be linked to the status of her sons. A women who gives births to only sons will have a high status while a woman who gives birth only to daughters will have none.
If men fought constantly, then women would likely perform most productive labor. That is the pattern in all low-tech militaristic extant cultures. However, that might conflict with containment.
Architecture would be based on walled compounds with the women/children's quarters in the center and the men's quarters surrounding. Men would likely sleep in barrack like arrangements.
It's likely that art and literary themes would be vastly different. Sexual beauty would not be an important theme. Romance would likely be unknown. Most literature and art would concern masculine power struggles and conflicts over status and loyalty to elders.
As the society grew more large scale (assuming it could given it's fractious nature) the most dominate male groups would have the most females. In groups with a lot of females, there might be enough females for each male to start corralling his own set away from the other males. At first, this might seem like a good way to use abundance to avoid conflict but eventually each male would stop looking at his relations as allies and start seeing them as competitors. Aristocratic male groups might be treacherous and prone to blow apart while lower class groups would be more mutually supportive and bonding.
As technology advances, there might be a subtle power shift if women did most of the work. As society became less violent, productive work would increasingly provide economic power and most of the work would still be done by women. The condition might be like the early industrial era with aristocrats still strutting around while the emerging productive class quietly took over. Men might still value fighting but fight little. They would likely just laze about. Superficially they would order women about and still control them sexually, but in all other matters women would maneuver men to do what the women wanted. Since men would consider all non-military matters as beneath them, this would be easy.
An obvious story potential would lay in some humans being born in each generation immune to the altering-effect and having the natural human mating pattern of always interested. Such individuals might be regarded as dangerous and be hunted.
A woman that was always sexually receptive would likely get raped to death if she couldn't disguise her availability. On the other hand, the magic wand pheromones simply might not ever manifest and no man would ever show any interest in her.
A male with sex always on his mind would likely be regarded as insane and prone to unnecessary violence. Out of frustration he might try to have intercourse with non-receptive females resulting in injury. (This happens in some over-bred domestic species of birds when the males lose the ability to distinguish when females are in season.)
If the reversions were relatively common, say 2% of the population, they might create a special caste for them and isolate the "afflicted' men and women together. They might develope some special task or function which only the reversions could effectively carry out.
If women went into estrous in sync with women near by, then all the women in a male group might activate at once. This could cause the male group to be vulnerable to attack. Male groups might divide into mating and guarding groups, likely based on lot or strict rotation. The mating groups would sequester themselves in the women's quarters for the duration and the guards would stay away for the duration.
Contrariwise, women in estrous could be used as weapons. If men lost control in their presence, then sending a few receptive women into a group of enemy males would make them helpless, if another male group could attack from outside of the range of female hormones.
That's about all I think of for now.