That’s right. Most people essentially use the Amex as their spending card, whilst also popping the money into a pot on Monzo - then just pay the balance off at the end of the month.
I’m sure someone will be along to correct me, but I believe AMEX pay all cashback in a lump sum at the end of every year.
An alternative would be Tandem, they pay a lower cashback amount (0.5%), but it is paid monthly. See: