It's rare to see a reproductive system which does not provide crucial benefits to the society, so I would expect to see a substantial reflection of this deep rooted reproductive strategy in their society.
If asexual reproduction was enough, complicated techniques like sexual reproduction would almost certainly not occur. Given that the system you want is even more complicated than sexual reproduction, it's not going to occur in a world where asexual reproduction is good enough.
Sexual reproduction has a lot of advantages. It's why, generally speaking, higher life forms all use it. Accordingly, we're going to need to find a reason in this alien environment why sexual reproduction has too many problems to be the one-size-fits-all solution.
You mentioned aphids, which unfortunately I know very little about. Fortunately, aphids are alone. Enter yeast, my brewer's little buddy. Like your aphid buds, yeast reproduces asexually quite often. Give it a nice big vat of soon-to-be-beer wort, and it'll replicate like mad. However, in high stress situations, yeast shifts reproductive approaches towards sexual reproduction and the creation of spores. (I'm handwaving a bit. Check out the real lifespan of yeast, its awesome!)
So while I don't think your creatures are going to be hyper-intelligent yeast cultures, I do think we can take something from this story. The yeast had to deal with a tremendous dynamic range of environments, from "doin' the backstroke in the wort" to swimming in an ethanol-derived antiseptic bath of their own creation. They vary the reproductive approach based on the strain of the environment.
So let's consider a few possible worlds where the stress could be so high as to warrant such a complicated solution:
- The society is usually female, except in times of famine. In a scenario like this, it makes sense to have the males be small lightweight drones. Normally, it's an all female culture, but when times get tough reproduction shifts to making large numbers of resilient but otherwise useless males which can go into the world and keep their genetics going.
- The society is usually female, except in times of great violence. At this point, they begin to birth males, which are genetically structured to be vicious warriors. This would piggyback on any interesting reproductive strategy, but the cultural ability to create tools of war in a few short years might actually dwarf the reproductive benefits.
- There is no society, most of the time. The world is too inhospitable to allow it. Everyone lives in isolation as hermits. However, every once in a while a society survives long enough to warrant switching over to to sexual reproduction, while the opportunity lasts.
In all cases, expect to see a dramatic environment which inspires dramatic approaches to survival.