Generally speaking (very generally), Romans did not force their customs their customs on conquered people. Obviously there are exceptions but ordinarily conquered people would have to pay tribute to Rome, which might include monetary taxes and/or having to provide soldiers during war, as well as during the imperial times the conquered would have to add the Emperor to their list of deities.

However, when it came to Economic and Political decisions, Romans would favor those who acted more like Romans. Merchants would learn Latin to better communicate with Roman Soldiers who would be stationed in the area. Political Leaders might dress as Romans to try and differentiate themselves when Romans needed to appoint someone. Businesses might cater more to Roman clientele, such as serving Roman cuisine or trading in Roman goods. etc. etc.