that is not all true and you have misconceptions there, every time a governor is appointed behind them was a corp of clerks and officials to keep the order and authority of Rome, they deal with the differences among the Native people and conquered cities, so they have the function of being a diplomatic-admin-military force to integrate them. In a time of warfare not all the Consuls were the main to lead a Roman Army, the Senate appointed to General with experience to do tasks too. How another way Octavian will be Emperor in a future if he barely had military experience and dislike the army life?? Agrippa and Mark Antony (in the civil war) did all that job for him. We can expect that greedy and overconfident generals/governors with Martial law, refuse to quit his task as the maximum leader on an army, but the common norm was that a lot of them delegate those task in subordinates. Scipion wasn't Consul/Governor when he was fighting the Carthaginians, neither Marius before his reform when he was with Sulla fighting against Rebels in North Africa.
While a Republican governor/consul would certainly have various legates and junior officers under his command (as you'd expect for any large military force), they were both absolutely primarily military commands and seen as such. His legates answered to him, and he was the commander of the army; even someone like Cicero (more at home in the courtroom than the battlefield) found it necessary to personally lead his troops against various enemies during his governship of Cilicia. It's also worth distinguishing between the role of a governor/consul in the Empire (or even the very late, on perpetual verge of civil war, Republic) from the period that I:R mostly covers (especially as the levy system, vs. the legion system to be revealed next week, is meant for the earlier, pre-Marian period).
The idea of a "Roman Province" as a land to be ruled over doesn't exist in 304 BC, when the game starts. The term "provincia" was used to describe the task assigned to each of the two consuls. It was almost always military in nature (so, a consul might have been assigned the provincia of Gaul, in the event that a war with Gaulish tribes was expected, or possibly even a specific Gaulish tribe like the Boii; they would lead their army to fight said Gaulish tribe, hopefully beat them, and win a triumph). The consuls were specifically invested with military authority by the senate assigned to a provincia (which, again, might not be a specific geographic region) and put in command of the army. They had other duties, but those were secondary and much less prestigious. Consuls who failed to achieve military success (ideally a triumph) were seen as failures, and as a result there was heavy lobbying/political maneuvering to be granted triumphs.
This explicit grant of military authority was limited to a few officeholders, of which consuls and praetors are the most significant. During the emergencies of the Second Punic War, we see a couple of innovations: the expanded use of proconsuls (originally consuls whose term has expired but are extended by the Senate, nominally in order to complete their task but also to provide a few additional commanders where needed, later other folks given acting consul powers), and a few non-officeholders granted extraordinary military authority (of whom Scipio Africanus in Spain was the most famous, and he was mainly chosen because no one else wanted what they thought would be a suicidal task). But in all of these cases, they are explicitly vested with military authority by the Senate.
It's not until the conquest of Sicily after the First Punic War that Rome starts using the term "provincia" to also refer to a specific area for administrative purposes. Even then, the older meaning of "provincia" as a task remains in use; Pompey was famously granted the "provincia" of subjugating the Mediterranean pirates, and Cicero later proposed to grant him the "provincia" of organizing improved grain distribution to the Roman poor. But we also see a newer meaning of more or less permanent geographic provinces spring up as well (starting with Sicily, then Sardinia, then Near and Far Spain, and so on), which were generally given to lower officers (such as praetors) rather than consuls, who initially still kept "provincia" in the older sense, as wars to fight/enemies to defeat and thus honor/glory/triumphs to win (although often now expressed in geographic terms; for instance Scipio in his consulship was granted the provincia of Sicily, with explicit permission to invade Africa if it seemed necessary, leading to the Battle of Zama).
In all of these cases, governors are granted military authority by the Senate (whether as praetors, consuls, proconsuls) and expected to use it where necessary. As Rome expanded, interior provinces (such as Sicily after the defeat of Carthage/Syracuse after the Second Punic War) became less likely to experience military action, and thus less prestigious, however border or rebellious provinces such as the Spains or Sardinia remained potential grounds for winning new glory. But that very paucity of opportunities means that the governors need to keep a tighter grip on the army, so that they can take advantage of any opportunities that do come up. Remember, there are many praetors governing provinces, but only two consuls at a time, so if you want to move up, you need to distinguish yourself somehow, and the best way to distinguish yourself as a good Roman aristocrat was to win a war somewhere. Indeed, it eventually became necessary, in the very late 2nd century, to pass a law prohibiting governors from taking their armies outside of their provinces without authorization (although this doesn't seem to have affected consuls), in direct response to various governors using their provincial armies to invade and conquer neighboring territories on their own initiative.
One of the Gracchi reforms in the late 2nd century had been to require the Senate to designate the consular provincias before the election of consuls; this meant they had to be chosen well in advance, which tended to favor the use of geographic provinces for consuls as well (since you might not know who exactly you would be fighting, but you'd know that a border region was more likely to give you opportunities for military glory), and also made them less likely to lead to military glory (since you might get unlucky and end up with a suddenly peaceful border and no opportunity to escalate). In addition, the decaying political situation in Rome (which led to things like Marius as consul using popular vote to usurp the command of the Jugurthine War from Metellus, not to mention more extreme things like proscriptions) meant that being absent from Rome was increasingly dangerous for consuls and ex-consuls. But by now we are moving out of the period that the levy system is meant to represent.
I am not a historian, but am basing my arguments largely on Drogula, Fred K.
Commanders and Command in the Roman Republic and Early Empire. Chapel Hill: The University of North Carolina Press, 2015