It didn't matter what the eastern Augustus thought, it was just a convenient fiction and the East never had any actual power over him

Titular authority in the region could pass to the eastern Augustus, a legal fiction that masked the emergence in the west of autonomous barbarian kingdoms which were now the successors to rome

even if the east rejected Odoacer, they didn't have the manpower at the time to invade and depose him and was suffering its own instabilities

..., as in the west, emperors in constantinople were fighting a losing battle against the expansion aristocratic estates and tax evasion on the part of their owners. Political conditions within Constantinople were periodically unstable, and the reign of emperor Zeno (474-91) in particular was punctuated by a series of conspiracies and revolts

In 484, the Persians waged war on the Romans once again too

So the east accepting it would atleast give them the appearance of control, rejection wasn't really an option.

Source is The Oxford History of Byzantium

There's a few good reasons that Odoacer would want to maintain a positive relationship with the Roman Empire and the Emperor out of Constantinople.

1. Odoacer himself had only recently come to power. He led an army of peoples that had formerly been under the Hunnic domain, those being the Scirii and Rugii (and the Torcilingi, which according to Herwig Wolfram was probably the leading tribe of the Scirii, like the Iuthungi were the leading tribe of the Alamanni). Germanic societies in late antiquity (in this sense, the 1st-7th centuries, not the typical 4th-7th century definition) were confederations built around a "chief" with some distinguishing trait or traits that made him qualify as a leader, one of which was oftentimes a favorable treaty with the Romans. Even in this era of "forming kingships" we often see cases where the other parts of these migratory milito-aristocratic classes depose or operate independently of their group's leader. E.g. Anaolsus in 431 campaigning against Narbona, which was apparently not sanctioned by Theodoric, or the assassination of Thorismund in 453, as his brothers were pro-Roman and wanted a more amicable relationship with Aetius and Valentinian III. By obtaining recognition from the emperor as the holder of a foedus and his people being official foederati and granted Roman authority, it maintained his position.
2. A further part of this was what we call Imitatio Imperii, or imitation of authority. This was basically the act of imitating the actual position of Roman emperor, in dress, mannerisms, etc. This was an important part of late 5th and 6th century Germanic culture, because these new leaders needed to project visual authority in the same way as the Roman emperors did themselves, to a majority Roman population. Remember, the incoming migrant groups were small, numbering only in the tens of thousands, entering a western Roman empire of 20 million or more Romans (albeit slowly declining). By entering into a treaty with the east, it helped legitimize this Imitatio Imperii as well, and he could claim he was a proxy of the emperor.
3. Obviously, not incurring the wrath of the Eastern Roman army. By 484 the Roman armies in the Balkans had partially recovered from the disasters of 447 and 468. Malchus, fr. 18.2, states the Roman army in Thrace numbered 10,000 Infantry and 2,000 cavalry, while the army in Constantinople (which possibly could have been two armies, the Praesentalis I and Praesentalis II) numbered 20,000 Infantry and 6000 cavalry in the period from about 474-480 (when the surviving fragments date to, although the whole work allegedly covered from Constantine through Anastasius). Although not quite the roughly 75,000 men that had manned the eastern Balkans (plus another 25,000ish in what would now be modern Serbia) this was more than enough to launch a campaign to retake Italy, the last of which had been done with roughly 25,000 men in 424-425 (the campaign was launched with two armies but one of the armies had sank in the Adriatic, so only Aspar's force was available).

Is it appropriate to call Odoacer a vassal per se? That's a difficult question. These foedera or treaties weren't actual settlements but more like the installments of client bureaucracies. The people settled first under Odoacer and then under Theodoric the Great did not actually receive land, they received the tax allotments from the value of that land. Although they often later forced the landowners to turn over equivalent allotments of the land itself. It might be better to think of Odoacer and Theodoric's "kingdoms" as a prototype of the later Exarchate of Ravenna, in a certain sense. They were the overlords of what was basically a continuation of the Roman bureaucracy in Italy, just under new management. Their "barbarian" armies were quasi-Roman field armies, to a certain degree. But their authority stemmed from the Emperor of Constantinople, and they acted in the Emperor's name. And when they didn't, and stopped heeding the emperor's authority, he sent Belisarius to enforce his demands on the region, which we think of as the reconquest of Italy (which it was to some degree).