Seems like Brown’s and Swarthmore’s wider definition of “first generation” makes it look like they more disadvantaged students than they actually do, since the kids of highly educated immigrants with non-US bachelor’s degrees tend not to be as disadvantaged as the term “first generation” is usually assumed to suggest. The California publics’ narrower definitions of “first generation” look like they are actually trying to define it in ways that indicate disadvantage of the type that “first generation” is usually assumed to suggest (though the contexts and definitions appear different for community colleges versus universities).
One could argue that certain types of tiger parenting sometimes found with immigrants with non-US bachelor’s degrees is a disadvantage, but that is not usually the type of disadvantage associated with “first generation”.