It helps if you've researched the culture tech that increases colonial migration. It also helps if you've got high population growth via medicine techs/inventions and health care laws (the only social reforms that I TRY to pass, rather than pass when I have no other alternative to reduce dissent). The immigration national focus provides a trivial boost.
When you colonize a region, there is usually an initial "flood" of migrants from your territory until the population density increases enough to stifle further migration. Once you convert it to a state, the migration ends (or possibly slows to an irrelevant amount), and you begin to assimilate some of the native pops into your own population group (if it's present).
Some colonies seem to attract a flood of immigrants from my core territories, others end up with practically none, or quite literally not a single primary culture pop. I'm not sure why one province will end up consisting of 75% of my primary culture, while the adjacent province doesn't have a single individual from it. If there's no primary culture pop present in a province when you turn the region into a state, then the natives don't have a group to assimilate into, and seem to remain as native pops.
In one campaign, I annexed a region of China. My pops migrated to a particular province in numbers, flooding it to the point where I had about a 20% cultural representation, but only about a 2% presence in a second province in the region, and not a single primary culture pop in any of the three other provinces. By the end of the campaign, that 20% province had increased to over 50% by assimilation, and the 2% to around 5%, but the others NEVER assimilated a single individual.
My assumption is that existing population density versus habitability, dissent, and financial opportunity all seem to factor into it, yet there is some other factor (or factors) that I am not aware of, which play(s) a significant role in choosing where to move.