What Swarthmore or Brown mean is “if your parents are clueless about the college admissions process, don’t have the tools to intervene on your behalf to plan ahead and can’t help you through it financially or with advice” but they phrase it more politely.
In other words, if your dad was a nurse in Germany or has a post O-level business diploma from Bangladesh yes the student is first gen; but an MBA, a foreign college degree followed by a PhD or engineering degree in the US, a top 15 degree from any country, by definition the student isn’t first gen.
Some colleges that consider first gen status look at whether the parent has a 4- year degree.
For Op: a parent attending graduate school anywhere means you’re not first gen.