Why would watching the same feed on Apple TV affect ad revenue? As you pointed out, CBS and FOX still control the broadcast and the ads.
Not if it's on Sunday Ticket they don't. CBS and Fox get money for OTA ad revenue and anything that THEY do with their online platforms. They don't get anything from NFL ST. If a viewer was watching Fox on their cable or OTA channel and move to NFL ST, that's a loss of viewership for them. All their contracts with advertisers are based on # of people they reach. Advertisers will ask for lower rates if they think they aren't reaching the views for the money they are paying.