I work at a credit union that seems to have a similar policy to this, so maybe I can help shed some light on what happened. What probably happened is that she ended up say $20 short in her drawer last night. This morning she got into work, printed off every single transaction and then did the math on which ones could have possibly involved $20 bills. Then she gave every single person on that list a phone call. That includes ones she gave out $20 bills to and ones she took it from. Because sometimes there really IS a person out there that says "Oh yeah! You gave me $20 back on accident and I've been meaning to call you, but I went through the line at 5 minutes before closing!" It's rare, but it actually does happen. At our company, the tellers DO call you, not the manager. The reason for this is because *they* are the ones who screwed up, which means THEY have to apologize to you not the manager. Though if you asked to speak to the manager, I'm sure they'd be happy to oblige.
They don't have any right to take that money out of your account unless you confirm there was a mistake made, at least to my knowledge. It's a bit different with a check as they should have the paper copy. The teller is just doing her best to make things right, and trust me 98% of the time that money isn't found. She probably asked you for denominations because she was say $20 off and you deposited $100. If you deposited a $100 bill, not 5 20's then she knows that it couldn't have been you.
Anyway I hope this clears it up some or maybe makes you feel a bit better