It all starts with subcultures
There are a lot of opinions regarding the nature and definition of subcultures. I think that for this particular question the most suitable criteria of a developed subculture would be self-identification as a member of a subculture within a bigger culture. This subculture must be perceived as different from the mainstream culture in some meaningful and distinct way. This difference can be rather small but it should be important enough for an individual to base their identity on it.
As the time goes by, subcultures might become mainstream in a certain region or within a certain social group. The differences also accumulate over time. The identification with subculture becomes stronger, while identification with previously mainstream culture is less pronounced or disappears completely. At this stage, we can talk about diverged cultures rather than just subcultures.
Developed and fast mass communications might slow down the process of diverging, especially if there is a well-working propaganda machine. In this case, the mainstream culture will evolve to accommodate new technology, social norms, etc. and to continue to dominate. The subcultures will evolve as well, but will not become fully dominant. They would also be likely to share many core values of the main culture. Of course, there can be countercultures, but they rarely have many members.
Modern communications also can speed up the formation of new cultures by spreading and reinforcing stereotypes, norms, and attitudes associated with subcultures. If regional stations work on strengthening local identities and highlight differences from other regions, the local subculture might quickly become dominant.
The timeframe is hard to predict since a lot depends on the original culture, cultural policies, media behaviour, and population mobility.
Why cultures might start to diverge?
Different environments create different lifestyles which lead to different cultures. Geographical location, population density, climate conditions, etc. will all contribute to changes in behaviour, attitudes, cultural symbols and meanings, preferences in food and clothing. For example, in tropics, it makes no sense to wear thick sweaters; in the early afternoon, the temperature is too high for being outside; the food spoils faster; there are more parasites. People living in these conditions would wear lightweight clothes, rest while it is hot, leave no food leftovers, and be especially accurate to avoid parasite infection.
'Us' vs 'Them'
Other changes will be associated with the development of a group identity. Groups can be based on location, occupation, ethnicity, religion, or whatever suits your story. Humans love to divide the world into 'us' and 'them'. And when they do it they come up with distinctive differences (whether they are real or imaginary). Some of the groups can actively cultivate and promote these differences. This process is similar to existing nationalistic movements. Moreover, these tendencies to intensify in response to globalisation and attempts of cultural homogenization.
Interestingly, modern astronauts often develop this distinction between 'us' (in space) and 'them' (the Command Centre) despite the rotations and relatively short time in space. Since our space technology is still in early development, this greatly increases the dangers.
Specialisation of a region is another important contributing factor. Mining, agricultural, and research communities differ in their lifestyles and mindsets. Miners might be more focused on technology, while farmers might be more attuned to natural cycles and weather. An agricultural community will also structure its life and cultural activities around crops (the same as in agricultural societies on Earth). A research community might be more meritocratic and open to novel ideas and practices.
A real-life example is differences between Californian urban and farming populations. While they live in the same climate and uphold many of the core American values, they are quite distant culturally.
Pre-existing cultural biases
Your original culture might have some biases that would lead to marginalisation of some groups. These groups will start to develop their own identities and subcultures. Often these subcultures will start as countercultures that aim to diminish the psychological impact of marginalisation on group members.
It is also important to note that 'monocultures' are not truly monolithic. There are subcultures within them. There is no guarantee that the balance among subcultures will be the same in all regions, especially if they specialise in some activity. Some aspects of these subcultures might become a part of the core values of one group of people but not the other.
There are plenty of other reasons for developing local cultures. In fact, it would be almost impossible to keep the original culture as mainstream without establishing a totalitarian regime. The colonists have to be moved around a lot and often to prevent local identities from forming. The state propaganda should be widespread and very persuasive. Local deviations must be suppressed at all costs. The conditions of living must be controlled in all areas, so they do not differ too much (consider differences in suburban and inner-city cultures in the USA). All education must be provided and regulated by the government to ensure appropriate socialisation and transfer of cultural norms, ideals, expectations, and taboo.