If my grandfather(for example) graduated college, I absolutely would not consider myself first generation college.
If it intended to refer only to immediate family, the question would be worded: “did your parents go to college?”. But it isn’t.
To be first generation to do something, no previous generation of mine did what I am about to do, as I see it.
Here’s an example I use, just to show what I mean. If Olivia Newton-John was applying for college and asked that question, what would she say? I don’t think either of her parents attended college, but her grandfather was Max Born!
If I were in admissions and saw she answered she was first-gen, then with that HUGE falsehood I’d throw her app out.
However there is sure a difference between first generation to attend college and first generation to graduate college.