Assimilation only occurs in states, not colonies. Colonial Migration happens in colonies, not states. You need to have enough of your culture's pops to move into the province by Colonial Migration BEFORE converting to a state, otherwise there will never be any Assimilation. Colonial Migration happens (or doesn't happen) on account of a tech that boosts it, as well as unemployed pops that are willing to move. Researching techs which boost RGO output eventually leads to a wave of unemployed farmers and miners. In the 1800's migration is usually pretty limited, and can be non-existent, but steps up gradually as you research the techs, and as your population grows and exerts more pressure to leave.
Once you've got enough of your own pops in the regional capital province, you can begin promoting Bureaucrats to get the 1% of your own culture into official positions and turn it into a state. THEN, Assimilation can begin in any province with an existing cultural pop of yours.
Note that in a previous game, I conquered a region of China early on. Over the course of about 50 years, two of the provinces acquired modest size pops of my culture, one only gained a few hundred, while the other two never saw a single pop of my culture that was out of uniform. After I was able to convert it to a state, the two provinces with small but significant pops of my culture began assimilating rather quickly. I ended the campaign with something on the order of 20-30% of my pops in the one province, around 10-15% in the second, but only around 1-2% percent in the one with minimal numbers of migrants, and ZERO in the two that didn't get a single pop of my culture by Colonial Migration. If you can't get your pops to move there by Colonial Migration, you'll never see any assimilation later.
That may mean intentionally making life hard on your poor pops, so they move. Granted, a lot will probably move to the New World, but at least you should see a few migrate to your colonies.