Once you conquer a province it starts with 30 years of separatism and ends once the years are over. If rebels occupy it, separatism is extended by 10 years. Separatism contributes to unrest within the province, leading to rebellion.
http://www.eu4wiki.com/Rebellion#Separatism
Humanist idea group has an idea that reduces separatism years.

You are unable to change province culture until separatism ends, so you will be stuck with negative local culture modifiers. It is best to have both humanist and religious IMO.

Also it's a good idea to place troops on the province with separatism becasue it reduces the unrest.

Try not to spend monarch points.

Upping autonomy will reduce it as well, but the trade off is lower income. If you can fight off the rebels, it may be best to do so, but sometimes you aren't in that positon.