On line banking - strange happenings when trying to transfer money.

Yesterday I tried to transfer cash from one bank account to an account I have with another bank. Not had any trouble in the past but this time, when it asked for verification via my card reader, for some reason the reader got locked out. I tried it from two separate accounts, but no joy. NOW, here's the strange bit.
I contacted my bank and explained the problem. The person at the other end told me that she could see both attempts as being sent, so this would mean that I had sent the payment twice. I asked how this could be if the card reader had denied completion of the transaction at both attempts. It could not be explained, but I was told that a watch would be kept on my account, and that in the meantime I should go to an ATM and use the Services Menu to unlock my card reader, which I have yet to do.
BUT, both yesterday and again today, I went on line to check the balances of all three accounts involved. In all cases, there is no activity showing on any of the accounts.
So why did the person at the bank's end see the two transactions as leaving my two accounts, particularly as the intended receiving account (different bank) also showed no activity? Quite puzzling.