For whatever it's worth, I detected no assumption that your father was an immigrant in the OP. It's worth dwelling on the possibility that no such assumption is needed.
Following up Asian American with a list of other immigrant groups indicates that assumption pretty strongly. If he wanted to highlight cultural differences from WASP society, he could have listed Black Americans or Southern Rednecks. It's quite clear that Blacks and Redneck society, despite being very different from WASP society, is "native" to America in a way that Asian Americans aren't in public perception.
The two groups you list face more discrimination than most Asians precisely because of the assumption you list: they're perceived to be native, and cultural allowances aren't made, but the cultural differences are huge.
That's especially true for what you call "Southern Rednecks," of whom you will find approximately zero at e.g. elite schools, mostly due to this sort of discrimination.
It is also possible that his leadership ability did not manifest equally in both settings, for example if he was more passionate about the military than his civilian job and/or if it was a better fit for his skill set.
Not to suggest that some institutions don't still discriminate against Asians etc, unfortunately. Hopefully things are changing for the better though.
It's called "team chemistry" not "team logic" for a reason.
His master chief was black, his executive officer was a woman, and his head programmer was white. He was universally loved in the Navy community, especially by his subordinates, and though he did ruffle some feathers with his superiors, I can't believe he pissed them off too much, since they even honored him with a full page cartoon of him explaining his achievement with two other O6s and an O5, and twice with the legion of merit, which you don't get (much less twice) if the admirals are displeased.