I studied some classics in undergrad and am embarrassed I can't speak to this a little more than I am able to. I certainly, at least, am able to start from the understanding that we're talking about a time in history that long-preceded the nation-state or modern conceptions of borders. That said:
I'm finally getting around to reading the Gallic War, and at least the first few books of it seem to be basically about Caesar's activities in affairs throughout Gaul from his home-base in Gallia Narbonensis--"the Province," which is indisputably Rome's, and had been for a while. One tribe is trying to make trouble with another tribe supplying food for the legions and Caesar has to run up and intervene; one tribe is trying to rile up the others against Roman friendship and Caesar has to run up and intervene, etc.
At the start of the book, before any map seems to regard Gaul beyond the Province as "red," Caesar seems to exercise some kind of suzerainty or overlordship over the area beyond the Province--he's guaranteeing the freedoms of certain tribes, warning others not the mess with them, receiving hostages, and exerting what seems like a fair amount of influence over their internal affairs. Was this kind of activity normal around other Roman border regions? Or was Caesar unique or unusual in his energy and ambition to go proclaim himself manager of an enormous cultural region by virtue of his supreme military resources?
At one point he receives the submission of several tribes of the Belgae way up north--at least in his own account, they seem to basically acknowledge Roman authority. Does that mean their part of the map is "red" now, in the Romans' eyes, or in ours? Did Caesar see them as part of Rome's dominions? Did the Senate or the people? Was that made "official" by the territory's organization as a province later on? Or did they not regard sovereignty as black-and-white Rome's-or-not-Rome's in these affairs? What legal or political standards were important to them in calling land Roman?
In other words, what was the legal-political status of most of Gaul between Caesar's conquests and eventual formal provincial incorporation in the very early Empire?
So, the first thing to note is those maps you're looking at are modern constructions. Maps (if they existed - the point is debatable) were not accurate. Itineraries like Skylax's Periplus were more common - If you start at place X and head down the coast, you find place Y and later place Z and so on. The geographies contain descriptions of the shapes of the coast in words, but no drawings survive. I think the earliest we know of is the map of Agrippa, which doesn't survive, and it seems to have been a map of Italy. For an example of what maps looked like when they started making them, check out the Tabula Peutingeriana - a 4th century CE map of the Mediterranean.
The second thing to consider is what exactly a Roman governor's job was. Provinciae aren't necessarily geographically defined spaces. My Lewis and Short (my OLD is boxed up currently for a move - sorry!) lists such definitions as office, duty, commission, appointment, command, sphere of action, as well as the more common definitions you might be used to such as "the government of a territory outside Italy by one who had served as magistrate in Rome." This last definition I'm uncomfortable with, because originally the Senate defined Caesar's province as the administration of the roads of Italy, so clearly provinces can be assigned inside Italy. I personally like to think of a provincia in this period less as a territorial space and more of a brief: a sphere of action for accomplishing a job. In that context it's not shocking that Caesar was building relationships with Gauls outside the Province if they contributed to his job.
Bottom line, I think those maps are modern scholars trying to represent Roman influence in a rather subjective way that Romans themselves would not have understood. Romans believed in imperium sine fine, after all. Lines didn't matter to them.