Does the payment go through when you hit authorize, or does it go through when you close the batch?
If you don't send a FTP overnight, it gets authed straight away and depending on your merchant it may get passed onto the bank overnight or straight away also.
As far as the Tessitura application is concerned it is as soon as you click DONE after the card payment screen
If you are using a controlled batch, I believe the authorization does not go through until the batch is closed. This allows for transactions to be deleted from a controlled batch while the user has it open.