DNA evidence has so far placed the Tarim mummies' origin to central Europe, and more specifically to the Alpine region and north, which was prime Celtic territory 4,000 years ago. The overwhelmingly best guess is that they were ancient Hallstatt Celts who had traveled eastward, probably on horses and wagons, all the way into the Tarim Basin (present-day Xinjiang, China). As to why they settled in a mostly deserty region is not clear. It's possible that the region may have been greener at that time. Also, they had traveled so far, and over mountainous terrain, that when they reached this valley, they decided to make a go of it. They seemed to have lived there for about one thousand years.
This was a world in which the population levels weren't nearly as high as today. For a good long time, they may have been the principal racial stock of the region, which was not Chinese or Turkic at that time it appears. A thousand years is a long time, and things changed. Today's root stock population is of Turko-Mongolian origin, of which these Celts were absorbed into. Blue eyes and brown hair seem to be somewhat common, with mostly far eastern features.
Upon arriving there, it's likely that they sent out scouts. They must have figured out northward was the mountainous Asian steppe which was even less hospitable, southward were the Himalayas, eastward were seemingly endless deserts and mountains, and turning back thousands of miles to Europe was not an especially attractive option either.
I think that China deserves some credit, as they are fiercely protective of their history. However, since this region is not ethnic Chinese anyway, I think that it makes little difference. It should be noted that these ancient settlers had knowledge of bronze metalworking, which was not present in China at that time, and it was thought that the Chinese developed bronze on their own. They may well have, as this area was still a long distance from China proper.The Tocharian culture existed in the same Tarim Basin over a thousand years after "the mummy people" had disappeared, and it's not known if there was a connection. The Tocharian language was a branch of the Indo-European languages, now extinct. After viewing some of the depictions of them, they appear to be much more Nordic-like than Celtic.