In practice, they had near total control over their provinces. Like mini-emperors in a province. Most governors, even the "good" ones, saw provincial command as a chance to make some money after the expensive bid for office (getting elected in Rome was fairly expensive and some positions, like Aedile, required out of pocket expenses for repair and games).

An example of the power they wielded, although this time in a way that benefited the people, is when Lucullus reduced the debt in the Asian provinces owed to Roman creditors and the Roman people (the area had risen up with Mithridates against Rome and stiff monetary penalties had been placed on them as well as Roman tax collectors exploiting them which had been part of the reason for the uprising, in the first place). This infuriated the Roman equestrians and the Senate. But there was little they could do about it, officially. He was in control. That a governor could make a unilateral decision that seriously impacted the money interests of important Romans shows how much power they wielded over their territory.

When Augustus took on sole rule of the Roman world, after the death of Antony, part of the rights voted to him by the Senate was proconsular command over all the provinces. At first for set number of years (10 year intervals) and then indefinite. So, he was stepping into a valid constitutional role that granted nearly unlimited power over the provinces. Such a powerful role consistent with that of an emperor (outside of Rome) existed and all he had to do was tweak it.

Technically, they weren't supposed to engage in an offensive war without consulting the Senate. There were a lot of ways around that. Caesar, for example, maintained the facade that his wars in Gaul were defensive.

Also, if they were engaged in corruption (which was the norm) or strangled the provincial people too much then the provincials could recruit a Roman, usually a Senator or at least of Senatorial class, to bring a suit against him in Roman courts. These happened all of the time but rarely resulted in conviction. One exception is the case that made Cicero famed, a successful prosecution of Gaius Verres, governor of Sicily. However, he was thought to be over the top in his corruption even for the time and Cicero was unusually gifted. Julius Caesar also made a name for himself in the early days by bringing these suits on behalf of provincials although without much success. However, these suits could only be brought after his term as governor was over. Like other magistrate positions, like Consul or Tribune, there was immunity while in office.

Romans were aware of the problem of corruption in the provinces. And had laws and measures to guard against it but they were largely ineffective. Little provincial administration took place from Rome itself.