Already in the Ist century BCE, Caesar mentioned the province of Gallia Transalpina as "our province" in Gaul in comparison to the rest of it : even after the provincialisation of these northern regions, southern Gaul (renamed "Narbonensis") was eventually kept politically apart of the "Three Gauls", as a public province whose proconsul was mandated by the Senate while the other were under the charge of a propraetor named by the emperor.
This institutional disparity highlights a great difference between northern and southern Gaul, already perceptible by the turn of the millenium.
The part of the Gauls washed by the Mediterranean is entitled the province of Narbonne. [...] Its agriculture, the high repute of its men and manners and the vastness of its wealth make it the equal of any other province: it is, in a word, not so much a province as a part of Italy. (Pliny,Natural History, III, 4)
Even before its conquest in the IInd century BCE, Mediterranean Gaul was directly contacted by Italian traders, its agriculture early on connected to Mediterranean features (such as an early presence of wine in the lower valley of Rhône) and open enough to Italian influences (as the rest of Celtic Gaul would be comparably in the IInd and Ist century), but the Roman conquest led to important transformative changes over it during the Late Republican era.
The land won by conquest over expropriated local peoples, considered thus as ager publicus, was largely redistributed to Romans settlers or agents as quoting Cicero, publicani, agricolae, pecuarii, ceteri negotiatores (Pro Fonteio XX, 46*) :* farmers from Italy, traders and managers for senatorial families or the state, etc. but especially urban colonies settled with veterans and other colonists as Narbo (one of the first Roman Law colonies outside Italy) or Aquae Sextiae that led to the disappearance of indigenous urban centers and to further control the country, highlighted by the formation of the Via Domitia, a roman road replacing the older way and connecting colonies and allies.
Local peoples, submitted, crushed or defeated (revolts as Tectosages in 107 BCE only giving more opportunities of direct control) were put on a backseat and their grievance essentially ignored or dismissed, as with the monument of bad faith and Roman prejudice known as the Pro Fonteio, Fonteius being blamed by indigenous people of extortion and brutal management but defended by a Cicero defending him against "those" people, impious and savage.
Whereas the Cesarian conquest of Gaul, although brutal, wasn't followed by massive expropriation and at the contrary was seemingly marked by a strong continuation of elites without much Roman/Italian settlement (a bit more than half, that is around 18, of Latin and Roman law colonies in Gallic provinces could be found in Narbonensis), Late Republican southern Gaul had been put under firm colonial and Roman control.
It is not to say that local populations were set in an apartheid-like situation, although it's not always clear how much they benefited or were damaged by the situation besides a case by case approach (with, in a same group, likely pro and anti Roman sub-groups), but they lived early on within cultural, economical and political frames utterly dominated by Romans, from land management to institutional organization further completed under Caesar and under his successors by creating new Roman and Latin law colonies (either settling veterans, colons or granting the status to indigenous centres as Glanum), Latin law being granted to the whole province ca. 43 BCE, that is a century before the Three Gauls.
This favourable status, along with a tight economic connection with Italy (the region becoming notably a net exporter of wine to the point Roman authority had to order rooting out local vineyards) and a prestigious way-of-life, was particularly attractive for locals especially for elites that eventually gained access to social opportunities : the vast majority of senators from Gaul during the Principate, for instance, came from Narbonensis (although dwarfed by those coming from Africa), Valerius Asiaticus was thus not only the first Gaul to become senator but even becoming consul twice.
Thoroughly romanized culturally, economically and politically, "their Province" wasn't much different since the Late Republic from Sicily or Cisalpine Gaul, at the notable exception these ended up being included within Italy whereas Narbonensis remained in-between sort of a Gallic province.
The provincial reorganization of the IIIrd century saw it being joined with Gallia Aquitania (the Rhône dividing Narbonensis in the west and Viennensis in the east) but while the Three Gauls had at this point be importantly romanized themselves and while the southern regions essentially shared the same cultural and economical fate than its northern neighbours, enough discrepancy remained (being relatively spared by the civil wars and the raids of the Third Century Crisis, notably) that the term 'Provincia' seem to have stuck out of habit.
Still more akin to Italy during Late Antiquity, the "gateway" between the peninsula and Gaul, the seat of palatial and monetary ensemble in Arles, where Christianity and Christian monachism was first importantly present north of the Alps, the Diocletian province of Viennensis ended up being the only part of Gaul still under, thin, imperial control in the late Vth century and eventually recovered as such by the Ostrogoths in the early VIth from Visigoths and Burgundians, Theoderic's chancery ending up calling the territory beyond the Alps from its old nickname, no longer as. This is when 'the provincia' became for posterity, from a long history of strong connection with Rome and Italy to a proper name, 'Provincia'.