Just as with savings accounts, it's definitely not reported if it's a small enough amount per year. I have had a Discover card forever, and I've never got a tax thing for the cash-back, but my cash-back has always been below the several-hundred dollars which I seem to recall being the trigger for interest income being reported.

Someone who gets huge amounts of cash-back annually on a card would therefore have to report whether they get a tax thing for their large cash-back.