The romans built colonias, city districts populated by romans, in each city they conquered. With time the administrative, military and technological language of the natives got more and more latin words. It was seen as sign of high education to speak latin and read latin texts. So the native culture was step by step reworked into one more and more compatible with the empires culture. Hermann the Cherusk for example, or "Arminius", as the Romans called him, the great hero of the german tribes, who defeated the Romans, was culturally seen in fact more Roman himself than German.
I think there should be a culture conversion after a given time. Depending on province/state religion, ease of integration (a Pole or Czech can integrate into the saxon culture much faster than a Berber or a Bantu), maybe stability and such things.