Typically, what happens is that when you create a clear social divide, the second class either doubles down on their own culture, or seeks to mimic the higher class. So, yes, the Romans pretty much went there an said "We rule you now, give us money". They occupied them, their merchants filled the markets, the cities, forts, and roads that they built were in the Roman style. In those cities, Temples were built to the Roman gods for the Romans who lived there. However, their approach to the local culture was more or less hands off unless it threatened Roman interests.
What this would have created is a situation where there is a clear dominator, with a distinct culture which would have percolated down to the occupied peoples. Because they had to deal with Romans and because Romans were the dominant culture, the people learned Latin. Because they could rise higher by working within Roman culture, they adopted their gods and integrated. In the most completely integrated regions (Italy, Cisalpine Gaul, Spain, and so on), the culture there became functionally Roman. However, it was a naturalistic development born of practical interest, rather than a culture imposed by the conqueror. Those tend to last longer in outlying regions.
On the other subject:
I would say one of the most important things to consider is that while they were both expansionist, socially stratified, and tradition bound cultures, China and Rome share virtually nothing else in common. I'm trying to think of how to expand on this, but as a rule, you can't really compare distinct cultures with one another. Everything from religion to history to whether the people share a generally individualistic or familial or nationalistic bent can influence how cultures interact.