The PRC requires that "The chairman of an autonomous region, the prefect of an autonomous prefecture or the head of an autonomous county shall be a citizen of the nationality exercising regional autonomy in the area concerned." http://www.npc.gov.cn/zgrdw/englishnpc/Constitution/2007-11/...
I'm not sure whether subdivisions in an autonomous area are automatically autonomous as well, but if so, that would require local Tibetan governments at all administrative levels to be lead by Tibetans.
That doesn't mean they can't use the old tactic of promoting officials across regional borders to prevent individuals from building up their own little kingdoms. E.g. the current chairman of Tibet is a Tibetan from Yunnan, so technically he isn't ruling his home province. https://en.wikipedia.org/wiki/Che_Dalha
> her father had been in the army, and upon leaving he was settled in Xinjiang.
How does settlement work in that case? Did they give him a plot of land to farm or a job at a SOE or did they simply order him to stay in Xinjiang and find some way to make a living there?
You're just asking for Tibet to revolt at that point. Obviously you know this, but longstanding imperial Chinese policy was that no official was ever allowed to administer his own home province. There was good reason for that.
> The reasons for each individual migrant choosing to go to Tibet instead of staying in their home provinces are more likely to be economic: better-paying jobs in tourism, mining, hydropower, ...
Some of them are just assigned as settlers by the government. I don't know how significant the phenomenon is, but e.g. a friend of mine told me that her father had been in the army, and upon leaving he was settled in Xinjiang.