You'll notice that Kay prods it out of him when he'd rather they listen to Johnny singing.

Anyway, one would assume that by this time in their relationship Michael has given Kay at least some information with regard to the kind of business his family is involved in, and which at this point he wants no part of. They may already be secretly engaged and he trusts her.

And with Johnny Fontaine showing up at his sister's wedding...why shouldn't Mike tell that story about the bandleader? It's a pretty interesting one!!!

Apple