The Roman Empire lasted a long time so it is hard to give a full answer to this question.

First thing to note is that of course there were quieter and more warlike provinces and how people felt about the emperor changed over time. Almost all provinces rebelled at least once against the Romans.

I will talk about the Roman regions as provinces because I think that is what you mean. But keep in mind that what Roman knew as provinces or “provincia” are not the same as our provinces. Provincia was a title that not every conquered region would get immediately.

Some provinces started out as rebellious but later became a backbone for the empire. An example is Hisspania; when Caesar served there as pro-consul it was rebellious but it became a very rich province in the next century and would provide a lot of new senators under Vespasianus.

In general living in Roman provinces was not that bad Romans accepted that local people held on to their traditions and did not force people to romanize. They did teach the local elite Latin and gave them education. When the local elite romanized the lower classes slowly followed.

Your second part of the question might be unanswerable. In Roman times people who wrote were the elite so the only way to know how the commoner thought about the emperor is through the local elite which will always cloud the reality