I don’t get this. It just oscillates to and fro and an extra Buy is quickly (in 3P game literally on T2) worth a Province. In a 2P game greening will start on T3 so the game will be over on T6.
At least in a 2P game, you would hesitate to buy AC as soon as there's six tokens on it, since your opponent would then be the first one to get a Province from it - and possibly the only one, since they can just wait until the last turn of the game to get the $8 Eye for an extra free Province. The game won't become a Province rush unless both players want it to.
I think it's an interesting interactive card in 2P. But I'd consider setting up the Eye with 2 or 4 tokens instead of 3, to make the first AC buy of the game a more difficult decision. With 3 tokens at set-up, if you're the first to buy the Event and it oscillates to and fro, you'll also be the first to gain a Province from it (since the token is added before the gaining).
But I agree that AC can be broken in multi-player games. There, if two (or more) of your opponents will just snatch it from each other each turn, you must join in if you don't want to lose.
It would be nice if the concept could be salvaged to also work in multi-player games. Maybe only allow a player to buy AC if their right neighbour has the Eye? That way each buy of AC would be a difficult decision instead of an automatic one in multi-player.