The current J2b in Tatars and Chuvashs is a young clade with older cousin clades in the Balkans and central Europe
J-Y12000, so it got there from the Balkans. Goths maybe, or Huns, I don't know, but someone in the early middle ages moved it there, that could actually be the pattern with other Balkan haplogroups as well, found in volga urals or deep beyond in the steppe, I can think of E-V13, I1 and some Balkan R1b-CTS9219, moved to the steppes from the Balkans, not the other way around.
However, that doesn't mean J2b2a1-L283 or a deeper subclade can't be Indo-European, ancient dna has been found that may support that, I have my doubts but still, extremely low frequency in Crete and western Anatolia doesn't suggest they took that migration route, like the Minoans I used to think Balkan J2b must have come from the same source, Kura-Araxes ? I don't know if Archaeology supports that, I'm giving that culture too much power :embarassed:
I would refer to
Trojet's post above, he said it better than me.