Most US VISA credit cards, at least from major issuers, should now work on TfL (but if your card has been in your phone for a long time, I would recommend deleting and re-adding it to ensure it has the correct provisioning profile). Some VISA debit cards, and possibly some obscure credit cards, may not work yet.

I think US Amex cards will eventually work, but not for a while. Amex made a choice when provisioning the cards in the US to maximise US compatibility while sacrificing non-US acceptance. As noted by tmiw, a physical Amex contactless card from the US will work though.