For info exchanges like this, you should always insist on calling them back at a number listed on their card or website.
If they cannot do that then its a scam or you should change banks
If they cannot do that then its a scam or you should change banks
Don't do this either. If the caller was a scammer, they can give you a number that would call them back, and now they have you "hooked" because you think you've called your bank, when you really called the scammer back.
Call them back on a number printed on your statements or a number you retrieve, independent of this caller, from the bank's website.