I think there is some confusion between the Citi Executive and Prestige cards. I had an attendant just wave me through when I showed my Prestige card, murmuring something about an Admiral's Club membership (which I do not have). I expect this will change when the attendants are able to swipe both card types, but then the problem should diminish as US flights become AA flights.
Yes, I noticed the same confusion twice last month while visiting the old US Club at DCA. Both times, after looking at the card, I noticed the agents trying to look up a membership using my Advantage number, at which point I had to explain that the Prestige card just gives me access, not an actual membership. The first time the agent just looked at the back of the card for awhile (thankfully it now says "Admirals Club Access") and waved me in; the second time there was an another agent who seemed to be legacy AA who helped out.... but it did seem like they had to go through several computer screens to process it.