They're referring to the Huns, not the Hungarians. They're two completely different groups. The Huns invaded in the 5th Century AD, and the Hungarians invaded in the 9th Century AD.

Both groups came from Asia. The reason why the Hungarians seem "local" now is that they've intermarried with local people for so long. But the language they speak is not Indo-European. It's actually related to language spoken in Siberia.