Since it's enough of a concern for you to have asked, I'd try the magnet test on the main frame tubes too. Then you'll know for sure.

I'm going to disagree with cyccommute about lugged aluminum frames. There was a window of time in which aluminum frames were commonly produced, even at the low end, by bonding the tubes into metal lugs. My Raleigh Technium frame is one of those. Your Schwinn might be one too.