The fundamental issue at hand is getting a response from the bank that processed the transaction to confirm that he transaction has successfully occurred. If you are just sending the user to a thank you page then you are not able to confirm the status of the transaction and have no guarantee that it was successful.
This is usually handled by some type of secure post back from the bank. In this return post there should be a unique identifier for the order that will let you know what order the return post is for. The idea is that before you send the user off to the bank site you record the order in a database using the store order summary and store order details server behaviors. Then when the bank posts back with a successful transaction you would update this order record to indicate that it was successfully transacted. At that point you can send the user or store operator an email receipt to indicate the successful status.
Unless the banks have a way to post back the details like this it will not be possible for you to confirm that status of the transaction. Also, if the status is not posted back in real time you will not be able to indicate to the user the status at the time of the transaction, so sending them an email would be the only way to inform them.
This is obviously going to require further custom development on your behalf to implement, but you should start with any development guides you have for the banks to see if this type of post back is possible and determine how it is implemented.