Well pannonian basin was like holy land for nomadic tribes. Pannonian basin has advantage for nomads since it is surrounded by Eastern Alps, Carpathian Mountains and Dinaric Alps. This gave nomads tactical advantage since they could easly defend themself in mountain passes from foregin invaders. Also pannonian plain was rich and has good agricultural soil. Many people already lived there. Nomads who came to pannonian plains usualy made alliances with people who already lived there like Slavs. Over time they soon adopted non-nomadic way of life but their languages began to dominate among other non-nomad people. With each nomadic tribe coming in pannonian basin the future language began to evolve and when the Magyars came in they made one of the final but majory contribution to the developement of modern Magyar language. After Magyars, Cumans, Jassic people and German settlers added their influence on Magyar language.

There were many nomadic or semi-nomadic tribes who came to pannonian plain such as;

Jassic's (possibly related to Iazyges but they came after magyars)

These tribes are either Iranic or Turkic and they definitely laid foundations for modern Magyar language. Beside these tribes there were also Slavs (who were numerous but not enough to absorb others), ancestors of ancient Romans and some Germanic tribes living in Pannonian plains. Since turkic tibes were strongest they began to influence others and slowly modern Magyar language began to evolve with storng slavic, iranic and other influences.

Anway back then tribes werent formed on ethnic bases so you have example of Bulgarians etc. Tribes were often confederations of people with same interests. For example one section of around 9000 Bulgars broke away from Avars becouse there was some dispute between them so they seeked new place to live in. First they went to Bavarians but Frankish king Dagobert orderd Bavarians to kill them all. 900 survivors pleaded Carantanian duke Valuk to help them and he gave them permission to settle inside Carantanian realm.