Glad you mentioned this. I went to a strong wealthy public high school with a high asian population (~50%?). When I was there, a lot of my friends were 2nd generation immigrants and their parents still spoke their native language at home. Their kids (my friends) were perfectly fluent/native in English but didn't do as well in the "edge vocabulary" parts of the SAT and I always figured that was why (in comparison to me and my english-at-home parents).
If English is not a student's primary language and fluency improves as they advance academically, up to a plateau with age.
Not sure if this was properly controlled in SAT studies. https://www.ncbi.nlm.nih.gov/books/NBK11007/