Bank of America display a best practise here, with money remaining in the customers account until the biller receives it.

Pay Bills With a Click? More Americans Are Doing It and Banks Are Loving It – New York Times

Earlier this year, Bank of America also changed its system so the customer’s money remains in his account until the biller has deposited the payment. In years past, the customers’ checking account was immediately debited.

Other banks are also developing systems where customers can pay bills at the last minute and have the biller paid instantly. Online Resources, an online bill payment and presentment company serving mostly local and regional banks like New York Community Bank
and Ohio Savings Bank, will probably offer such a feature to its
clients early next year, according to Matthew P. Lawlor, the chief
executive.