Made contacts at banks, now what?

I've gotten into contact with around 10-15 alums at various BB's, looking to get an internship in S&T, and have had some good 15-30 min conversations with them over the phone. They seemed to like me and were receptive to helping me out or talking again in the future.

The question I have now is where do I go from here? What is the best way to turn these contacts into actual interviews and when should I go about reaching out to them again or having another talk with them given that internship recruiting will fully start in a few months?

I am a bit confused whether to wait until these firms post on our career site or come to campus or whether interviews can start happening sooner. Any advice regarding this would be greatly appreciated.