There is an excellent book called “Alaric the Goth” by Douglas Boin that goes into a great amount of detail into the cultural shift. A big shift was when Honorius stripped freedom of religion away, this served to move Roman society towards Christianity and reinforced the view of the tribes as barbarians.
And correct, actually incorporating non-Romans into the military was a great way for those tribes to attain a stable life after since they enjoyed the same benefits as Roman soldiers for their service. When that was stripped away, they also would be subjected to terrible treatment and often had poor provisions.
JFC how hard is it to look up the sack of Rome? It was the Visigoths led by Alaric I, not the fucking Vandals. We see this referenced all the time here and each time it is fucking wrong.