When would that origin have been? 2800 BC seems late.
Don't know. In 2,800BC they were still there, the dispersal obviously would have begun earlier than that date. The first Asian skeletons only began to show up in the area in about 100BC.
I will quote from The Tarim Mummies by JP Malloy And Victor Mair:
"Narain argues that once one accepts the equation Tocharain = Yuezhi, then one is forced to follow both the Chinese historical sources and the geographical reference of their first cited historical location (Gansu) to the conclusion that they have lived there 'from times 'immemorial'. Narain infers that they had been there at least since the Qijia Culture c.2000BC and probably even earlier in the Yangshao culture of the neolithic. This would render the Tocharians as virtually native to Gansu (and earlier that the putative spread of the Neolithic to Xinjiang) and Narin goes so far as to argue that the Indo-Europeans themselves originally dispersed from this area westwards."
The extinct Tocharian (Indo-European) language is most closely related to ancient Celtic.