The Caucasians have always been in China and predate the Han themselves in the Gansu region.
From the excellent book The Tarim Mummies, page #281:
"...Narin Infers that they (Caucasians) had been there at least since the Qijia Culture of c. 2,000BC and probably even earlier in the Yangshao Culture of the Neolithic. This would render the Tocharians as virtually native to Gansu (and earlier than the putative spread of the Neolithic to Xinjaing) and Narin goes so far as to argue that the Indo-Europeans themselves originally dispensed from this area westwards."
The movement of the Romans to the Gansu region was a reintroduction.