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.
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.