Sounds a bit dodgy to me - she really didn't sound prepared for the phone call! Working at a bank, before I call a customer, I make sure who I can speak to regarding the particular account, so that if someone other than the customer answers I know what I can & can't say. If I were her, and I was calling regarding an account in your DPs name only, I'd only have said "Hi, this is Kaytee from the bank (not giving the bank's name), is DP there?" If he wasn't there and I knew you weren't a signatory on this particular account, I'd leave a message with you for him to call me back. I usually have the customer's mobile number though, so I'd give that a go, but I wouldn't go asking you for info, and I definitely wouldn't say

Give me a minute ill have a look through the account and see if i can talk to you about this.....your name is here but there is no where saying i can talk to you..
And then have a little chat to myself about it! Because obviously that's going to bring up questions for you, and if this was a confidential thing for him she's kind of letting the cat out of the bag.

When your DP does speak to her, if it's something you're supposed to be talked to about (which you probably are seeing as your name's on the account) I'd get him to ask them to make you a signatory, and then ask her to be much more careful with giving out/obtaining info in future.