As long as they moved in, created settlements, conquered, made treaties with the locals and hen over time became the dominate culture.
It is, after all what happened when the Indians arrived in Europe about 5000 BC.
About five groups left of the original inhabitants, the Finns, the Hungarians, Estonians, Basque and Sámi.
So it has been since the beginning and so it shall ever be.
The Hungarians were Magyars that immigrated into the area from the Asian plains into central Europe. (what with me being Hungarian Ashkenazim and all, got taught my heritage)