Isn't some of it have to do with it being a self selecting sample? If you come to America to study, you were a good student in your resident country leading to more chances of success than the average local citizen. Their children might be smarter on average.
Alternatively if you are coming fleeing persecutions you are enterprising enough to set up something for your children. That hard work inculcates a sort of work ethic in such children which in turn sets them up for success.
Speaking from experience as an immigrant myself.
I think all those are true, but if so the percentages of first-generation immigrants should increase as you ascend the educational pyramid. I believe it does from
undergrad to Phd, but not from general population to higher education, so clearly there are at least two very different worlds.
There is a motivation that comes with both trying to make it and being cognizant of the relative opportunity that is absent in the second-generation and beyond.
There are also many advantages given to students outside the majority. When those advantages land not on the disadvantaged but on the advantaged-but-foreign, are they accomplishing their objectives? How bad would higher education have been in Europe? What is the objective, actually?