to close on this: check in at MAA was overshadowed by a broken ticket. Unable to online check-in, but in the end nobody at MAA cared about anything testing documents.
I would like to add that i was impressed how the airport staff tried to help, even though in the end i needed to call for a reissue of the ticket before it worked.
tldr: was not asked for any testing paperwork on the domestic segment (even though they handed me a BP for my connecting with international segment - which turned out not good to travel).