If you plan to go back and play any of the older CoDs to receive one of the new prestige tokens, Remember to play at least 1 game completely thru after you have hit the button.
The servers will not record you hitting the button. They will only record what level you are on after you have completed a game.
The only way for the system to know you have prestiged in any of the games is to have played a complete game with the new prestige.
So don't hit the button and call it a day!!