All my controllers don the same. I think what I'm going to try before I play again is to put in another game like black ops 2 where it has many different controller styles and I believe it has one that says flip R1R2.
When I first purchased the game it was fine, recently I had to change my gamer Id (ex made it and it was 'Ladypebbles89' and current girl hated seeing it so..) which for some reason I couldn't sign into one and out the other so I did a restore and started fresh ( lost all my downloads and games I paid for) and since then I've had this problem. Lastly before I go I will say that I haven't played Andy other games since the restore.