[Cronos]

The Huns cam from an area around what is now Ukraine, more than 1000 years before the incursions of the Mongols. Many Huns settled eventually in what is now Central Europe, and specifically in Hungary.

Then how come the Huns are spoken of in China at the same time they were invading the Roman Empire and a branch of the huns, called the White huns were invading north-western India?

[John Valentine]

Steppe peoples were nomadic, cohesive, tribal, and wide-ranging. It is not beyond reason that they could have made appearances in all these places.

And when you say "at the same time" you don't really mean "at the same time", you mean "around the same time, say plus or minus 20 to 50 years, don't you? I'm not saying that the SAME groups of Huns atacked the outposts of the Roman Empire and outposts of China or India at different times, but as the main groups moved around it is highly likely that their presence would be felt in widely displaced locations.