They will soft pull all the time to make sure you are still credit worthy, and you do authorize this somewhere in the T&C of the cards you have with them. The soft pull will not hurt your score and is not visible to anyone else.

I don't know what service you are using to review your credit, but I sometimes get strange alerts on True Credit. It could be Amex updated account information or something and they alerted you to something that really does not matter. Also, if you recently (within a couple months) did open a new account, sometimes it will take a while for the account to show on your report. The inquiry is instant, but the account information takes from a day to two months to appear depending on the bank.

If it is a new hard pull, you should contact Amex to check into it to make sure you don't have identity theft in progress.