It sounds like your personal card has extended payment terms, thus the "due date" as opposed to "please pay by date". To stay on Amex's good side I wouldn't make it a habit of paying after the "due date" but once in awhile you are fine.
I was just thinking of this. Maybe there are some items that are being paid over time?
Yes, I received an offer from Amex to apply for the extended terms service and went for it but truth be told, I´ve neved used it. I´m even thinking about cancelling it.