If I were to go by the definition given above, "What I'm about to suggest will not be backed up by any dictionary, but I think of it as more a matter of cultural assimilation. If you see a parent ask their kid a question in their native tongue, they're first generation. If the kid answers in English, they're second generation."

I was 1st generation then changed into 2nd generation. I spoke fluently as a child, but grew self conscious of my pronunciation and my sister's teasing me, so I stopped speaking in Italian. Obviously you can't just hop a generation! My understanding since I was a child is that my parents are naturalized citizens and I am 1st generation American. I wish it went by how I felt because I would have dual citizenship right now. :-)