We really don't know anything exact about this group before the crossing of the Rhine. The three groups who crossed were described as Suebi/Suevi, Vandals (Hasdings and Silings) and Alans. It seems likely that they had first gotten together somewhere in the area of modern Austria, Czechia, Slovakia and Hungary, where various Vandals and Suebi had lived for centuries, and where Alans (and Goths) were amassing in this exact period, partly under pressure from the Huns, who were not yet under Attila's rule. At some point, the Huns themselves moved into position near this part of the Roman frontier.
Each of the groups who went to Spain came to be led by "kings" but we don't know if they started out that way. Also, we don't really know what exactly "king" meant to the Roman writers who used the term in these years. The word had long been out of fashion, but it is was suddenly brought back to describe men who were, at least in the case of Alaric the Visigoth, originally seen as Roman military leaders over groups of recently immigrated barbarian soldiers, and their families, moving around within the Roman empire.
There is debate among historians these days about whether such kings owed their positions to their Roman status. The older idea, which is now doubted, was that these kings were simply just the legitimate heirs of families who had been ruling over the exact same peoples outside the empire. They probably did come from noble families, but it probably wasn't so simple.
To put it simply, these peoples were probably not simply from outside of the Roman world, but rather from the militarized border, where barbarians were amassed. At first many of them were recruited into the Roman military, but after 400 leaders such as Alaric, began to be seen as kings of barbarian peoples, and not just generals ruling over mixed barbarian Roman forces. This is clearly because they started had started acting more independently, having been unable to get themselves considered as Romans.
So it was probably mainly the Romans who were originally the "go betweens" who created these amalgamations who they then used in their military. People like Hermeric had probably worked, together with his soldiers, for Rome. It was the Romans themselves who also seem to have developed the idea of giving such groups a part of the empire where they could live.
To what extent did these new kings see themselves as legitimate military governors of Roman provinces? In fact that seems to be the main way they presented themselves at first. Of course the Romans were not making it simple though, because they were by this time constantly fighting each other in factions, and the military units were constantly being called upon to take sides. It was often no longer clear who the proper boss was, above the leaders of various military units (both Roman and non-Roman).