ok.
can you please stop referring to the uighurs as indigenous people? it's simply a false statement - historically, ethnically, geographically, culturally. it's just wrong.
in both cases, we're dealing with invading tribes that entered the region in the middle ages. it's not even ancient history. the displacement is recent.
these are the people that are indigenous to the region, and they no longer exist because the turks killed them all before they moved in:
turkish-speaking people occupy a rather large part of central asia, today. they are indigenous to almost none of it.