Your suggestion that Asian-Americans are under-represented in US universities sounds wrong to me — more likely they are an "over-represented minority"
To really answer this question in detail, you'd need to clearly specify the scope of interest (i.e., which set of universities, which fields, etc.) and get admissions/employment data to compare with the demographics of the host population. Your choice of the specific group of Asian-Americans is also somewhat curious (and could be considered cherry-picking), insofar as it combines a race/ethnicity with citizenship status. In any case, doing a proper analysis of this issue would be quite a big project and I do not propose to make any attempt here to take that on.
Setting aside that caveat, if you are confining attention mostly to the most elite universities in the US, or the STEM fields in most universities in the US, there is pretty clear evidence that Asians are heavily over-represented relative to their population numbers. This is a consequence of what the economist Thomas Sowell has referred to as their status as a "model minority" (i.e., a high-performing racial minority with a number of high outcomes across various social indicators). You might be interested to know that a recent lawsuit against Harvard university involved a controversy over anti-Asian discrimination occurring as a result of affirmative action for other race groups. The materials in that case show that Asians are already heavily over-represented in the university, and would be more so if not for favouratism of other race groups on "diversity" grounds. An internal report at Harvard University in 2013 found that Asian-Americans were 19% of the student body, and if the university were to assess admissions applications purely on academic factors, they would have been 43% of the student body (see e.g., news coverage of report here).
So, your hunch here sounds wrong to me. Whenever the matter has been subject to analysis of admissions data, the results have generally shown that Asian-Americans are heavily over-represented in university admissions. Harvard is certainly not an aberration from the norm on this issue. It is certainly possible that Asian-Americans might be under-represented as students in some sub-fields, or at particular universities, but the general stream of evidence is the opposite of what you are supposing. As to faculty positions, I'm not sure there, because obviously it takes about a generation for students to flow through to become faculty. It might be that high numbers of Asian-American undergraduates have not yet flowed through heavily into higher degrees and faculty positions, but at least anecdotally, in the STEM field my observation has been the opposite.