Fusebill's integrations with e-Check gateways (ACH in the US and EFT in Canada) always assume that a successful transaction result from the gateway means that the payment has been received. Fusebill will mark an invoice as "Paid" in this situation, even though the bank may take several days to clear the transaction.
You will need to monitor your gateway's payment status to determine if the transaction has actually cleared the bank's process and has been finalized with the system. If a transaction is returned as "NSF" (non-sufficient funds), you should update the record in Fusebill to indicate this.
Usually, the best practice is to process a cash "refund" against the invoice to reverse the effect of the "successful" transaction (note, do not reverse the charges first). This will return the invoice to an "unpaid" state and you can attempt to collect the funds again; or, you can write off the transaction if you determine that the funds are uncollectable.
See Managing NSF Transactions on ACH Payments for more information.