We're not talking about the same things. First, I'm talking about all of Asia, from India, to Southeast Asia and North Asia, not "just" China.
If you are born and educated in a country and gone through the rigorous standards that they have gone through and reached the pinacle of recognition, first by going to the "best" HS, the "best" college, and "best" graduate program before being encouraged to pursue a PhD in STEM studies, it is very unlikely that the future expert will want to switch program and add to the challenge of getting a PhD abroad. Most top of their class will study at home and may choose later to further develop their work by doing stints abroad in post graduate studies.
Those who are 2nd tier students who may not necessarily be accepted at home will look elsewhere for the opportunity to get their PhD. Since English is the de facto global language, most of these students would end up in universities of the Anglo world. All of this is straight forward really.
As for Xi's daughter, she studied for a BA in psychology, completely outside the scope of my argument.
https://www.imo-official.org/countries.aspx
The world top 10: