Based on my own calculations, no, the per night rate shown on the AAA website does not include the tax.
When you look at AAA's website, they not only show the rooms that they have discounted availability for, but they also may show availability at rack rate. You can usually tell by whether the per night amount is an even dollar amount like $250 (rack) or an odd amount like $267.75 (discounted). When I have been comparing back and forth between Disney's site and AAA's, the total cost on Disney's site includes tax, but the price per night on Disney's site does not (that new per night price that shows below the room description). That per night rate matches the per night rate on AAA's site for any rooms they are not discounting. I've never done a complete booking on AAA's site, so I don't know at what point in the booking that they would show the rate plus tax.