Impossible to answer. You would need to look at each individual case, as the factors involved in how individual cities behaved towards Rome were as varied as the cities themselves.

As a case study: In 88/87 BCE, King Mithridates of Pontus invaded the eastern Mediterranean and sent his general Archelaus to Greece to take control there. Athens had been under the de facto rule of Rome for some time, but there were no Roman forces around when Archelaus and his army/fleet came knocking. Athens had a choice to make: stick with the Romans and actively resist Archelaus (and almost certainly lose the city outright, or else be besieged by land and sea), or acquiesce to the side that had forces on the doorstep and hope for the best. The Athenians chose the latter option, and unfortunately it did not go well for them in the end. Sulla came, besieged the city and its eastern garrison, and eventually burned the city and destroyed the acropolis. Did they "know" all along that this Mithridates had no chance against the Romans, and that eventually Rome would clean up and punish the Pontic sympathizers? Who could possibly say? They made a decision which kept them alive in the short-term.