It depends what we mean by "rising up".

If we're talking about the appearance of Barbarian tribes and coalitions of tribes, forming eventually whole peoples along the border, this was a phenomenon as old as the existence of a limes clearly distinguishing the territories controlled by the Roman state (what was eventually called the Romania) and the places that weren't (the Barbaricum).
While the border was quite static and "unnegotiable" (which was a departure from pre-Roman entities in Northern and Central Europe), it remained a porous limit and it was more about controlling the flux than anything : the trend by the Ist century AD onward was to regulate moving populations at the periphery.

These exchanges took the form of trade (both from Romans going in Barbaricum, but as well Barbarians going in Romania), Barbarian cross-border workers, Barbarians as military recruits, Roman "advisors" (a possible example of this had been found as far as modern Poland) to enact rear alliance against hostile groups, spies from all sides, raiders and counter-raiders, etc.

All of this led to a social, economical and political sophistication of Barbarian tribes, who became more like early forms (if definitely lacking in stability) of states. On this regard, this development of the immediate Barbaricum was already happening by the Ist and IInd centuries AD, way before Romania was split.
The border being an attractive region, groups (probably bands as well familial groups) moved southwards and westwards to it, as far as peoples living in Eastern Europe or Pontic steppes (proto-Goths, Sarmatian peoples, etc.)

The first big issues came from the ongoing political, social-economical and military crises in Romania, since the second half of the IInd century, and critically with the Third Century Crisis. Parthians and later Sassanians attacked the eastern borders and while Romans managed to repeal them, they suffered significant defeats without most net gain. Romans had to deal with this threat first and pulled part of their bordering armies out of the european limes to reinforce their eastern armies. Since the late IInd century, an institutional innovation appear with the co-emperors : generally but not systematically sons or close relative to the emperors, they are trusted with imperial responsibilities if not the title; in order to allow a more efficient political execution. At this point, we're rather considering a delegation and a preparation to supreme power, and not a collegiality though.

Barbarians, that due to the economic crisis had a lesser access to Roman trade and economic benefits that shaped a part of their material identity, began to form leagues and coalitions (including newcomers mostly in the Danubian region, which is not obvious in the Rhenish region) to better organize themselves raiding less defended European borders. Raids and piracy became commonplace and provincials began to accuse the Empire not doing its job protecting them and not being even able to use efficiently provincial resources in the East, the state being further decredibilized by the conctant civil war.
The Empire began to split in facts, with the constitution of autonomous "co-empires" in Gaul and Orient, that Rome is unable to break away immediately and temporarily tolerates as if it escapes imperial supervision, it's not necessarily unefficient. Aurelianus would deal by crushing the threat of a Palmyrene takeover, and negotiate with the last Gallic emperor as the general situation improves. There's a certain political hesitation for some decades, but as the whole system worked well enough in protecting the long borders of the Empire, it was institutionalised and tentatively systematized under Diocletian, what we call the Tetrarchy, dividing the Empire into fiscal-military ensembles, whom autonomy was personally delegated by the emperor.

It did have significant limits however. The dynastic logic still prevailed in the army and the imperial challengers, the centrality of the imperial palatial court in the making and destruction of careers, and the refusal of subordination led to several usurpations and conflcits until Constantine I became sole emperor.
Still, even in this situation, the borders remained stable enough, and the institutional reorganisation did worked out. In fact, the imposition of a dynastic imperium in Romania did managed to stabilize and reinforce the co-imperialship, by actually enforcing the idea of a collegiality rather than subordination (even if you can still point to a senior emperor more or less regularly). Dynastic conflict certainly continued, but overall, the system worked, not as it was meant to, but adressing the issues it was supposed to : the defeat and death of Julian against Sassanians simply didn't have the catastrophic political consequences than Valerianus' death had in the previous century.
It continued to works more or less efficiently with the Valentinian and first Theodosian emperors, and huiliating defeat of Valens at Adrianople owes little to the presence of two emperors, than Valens bad assessment and bad management of the crisis (not giving it due attention, not being able to wait for western reinforcements, among other things).

Another limit, eventually, proved to be much more problematic dealing with Barbarians, and especially Goths, within Romania : far from being mere tribes or coalition, they represented Roman armies and a militarized people that since having established they were able to crush the imperial armies, didn't shy away of asserting their interests and renegociating their status and their pay when they felt necessary, acting as any breakway faction in the Empire, looting their way to pay themselves and press the emperors into negotiation. (Now, there was as well the case of relatively quiet and loyal federates, such as Franks; Goths benefiting from an important prestige in this matter.)
The polarisation on two courts, one in Ravenna, the other in Constantinople; the absence of a real dominant emperor over both; made courts and Roman elites acting according the interest of "their" half rather than attempting an entirely collegial entente. It doesn't mean reinforcements or support stopped, but each court tended to have their own diplomacy, their own politics, etc.

For instance, while Constantinople relied less on Barbarians armies and support due to a wealthier fiscal pool; Ravenna generally depended on relations with them : the victory of the "anti-Barbarian" in Constantinople more or less reinforced the imperial authority, while its victory after the death of Stilico proven mismanaged and catastrophic for Ravenna.

Important officials began to play one court against the other, such as Rufinus or Alaric, to increase their local power and benefit from a better negotiated treatment; while Ravenna is unable to intervene legally in the Balkans and eventually elects to let Constantinople deal with his own issues, the grey area between borders benefiting to Goths eventually, which could switch from one raiding and intervening zone to the other without much hassle, something that Huns did afterwards.
Eventually, both imperial courts acted as independent governments, sometimes allied, sometimes outright hostile to each other, often focusing on their own business. It didn't prevented some collegiate actions, as the failed tentative to take back Africa (although it's far from obvious that Constantinople really planned to give the provinces back to Ravenna would have they won), but the general idea in Constantinople was that western Romans were unreliable; and in Ravenna that eastern Romans weren't that better than semi-foreigners; a situation that greatly beneficed Barbarians in the west, able to tie more direct links with Ravenna, to act as imperial subservient states and not meeting the full strength of two halves of Romania, except in Africa for very specific reasons

It would be wrong to consider that Barbarian political build-up was directly caused by the various splits of the Empire as such, being a mix of structural development and political opportunism, and for the most part, the system seems to have worked well enough in the IVth century. On the other hand, the effective split between Ravenna and Constantinople due to imperial minorities, regency of strong men, and growingly distinct political interests did allowed Barbarians to up the stakes and in the West, to be in a situation of strength (not just militarily, but as well politically and diplomatically).