You can still make the payment "today" and select tomorrow as the payment date for your scenario. Or any day in the future. Just realize AMEX will calculate due dates and interest accordingly.

In your scenario above, it is also common for banks to reconcile at day-end. Meaning, all the debits and credits are added for a day, and if your bank is nice, after applying credits first, they then subtract debits for day-end balance. In that sense you can "overdraft" an account as long as it's fixed by end of day.

In this case, ACH payments are once a day. Simply put, there's a cutoff time where they have to submit a transaction file. Most banks cut off crediting same-day payments at like 7pm or so for this reason. It sounds like there were cases where previously AMEX would take a payment too late to make it in the days day-end transmission, but still willingly credit it to your account that day even though they did not have the money until 2 days later. Perhaps they improved the efficiency of that process as after all you are giving them approval to withdraw on a date, not the next day.

Like any other payment method (such as a check), they don't get credited for the payment posted to the account until the following day.