I think I solved my problem. I think this rule will assign all conversations with leads to my "Admissions" team. If any conversations with leads would not be assigned automatically to the "Admissions" team with this rule, please do let me know.

P.S. I was confused by the word "customer" here. I conflated the concept with "users" because all my users are paying clients and my leads haven't paid anything so I didn't think of them as a "customer".

@harry w​ Nice to see you solved it yourself.