Once we become aware of the death of a customer and determine that the spouse transferred funds using the online credentials of the deceased from the account to another account do we need to transfer the money back? The money went into another account owned by the deceased to cover automatic utilities debits, so it was not transferred under bad intentions.

It is an unauthorized transfer, but I would wait until someone like the executor or executress approached the bank and asked them to undo the transaction at this point.

how is the account titled?

The account was titled in individual's name without a POD.

Then I would contact the spouse and let them know that you are restricting access to all of deceased accounts until whoever is handling the deceased estate contacts you.