Uh, I'm not a scam prevention expert, yet I would NOT have followed your steps. If a bank (or ANY entity) calls me up claiming to be X, I usually ask them what the issue is, then hang up and call the number listed on my card, the official website or documentation, etc.
You should never give out ANY information on the receiving end of a phone call. Period. Ask what their name is, what department they are in, hang up, call the number you were provided prior, and ask for the same department/person and describe the details of the call.
You should never give out ANY information on the receiving end of a phone call. Period. Ask what their name is, what department they are in, hang up, call the number you were provided prior, and ask for the same department/person and describe the details of the call.