Trying to play this version with Steam.
My Civ V will allow the cheats to work as far as I have seen so far on Turn 1 but you never can go to Turn 2+...the turn stays forever as waiting....so I guess the cheat is busted as the only thing I did was to click the movement one so I could search for a bit more to settle down first city. I tested it with cash one and reserach/unit etc....seems to work (cant tell since I am stuck on Turn 1).
Waited for 8 mins for my turn to come but it never updated and had to close down the cheat/game. When I played it without the cheat, it worked perfectly in updating the turns.
ver 1.0.1.511 Steam
Turn off Unlimited movement before letting the AI have it's turn. This is probably what is causing your problem. The AI will move forever otherwise.