I also used Amex and I saw the initial charges on Sunday for both of my iPhone SEs and Apple Care. I have a notification set to notify me via SMS any time there is a charge when my card is not present. I currently don't see any charges to my account when checking via the web.
I see both iPhones on my support profile, I have received the AppleCare emails, and I have received the shipping notifications overnight. When I check Apple.com for my orders, I don't see any errors when I check the Order Details link for each phone. It correctly shows my Bill to information and indicates that I used Amex and the last four digits of my card number.
What do you see on Apple.com when you click on the Order Details link?
Dave
Status Shipment Picked Up March 29, 2016
Shipment Issue - please contact Apple March 29, 2016
It looks just like that. Almost like there was initially an error and it was fixed and the item shipped. I got the official apple email and the tracking via UPS shows delivery tomorrow. It also shows in my support profile. It is reassuring knowing others with amex are having issues with the charge not showing. I also have the "notify me of charges when card is not present" turn on.