I took a quick look at the game. Seems simple enough despite the intriguing concept.
I don't know the exact logistics or have enough time to mess around to create a working prototype, but the basics would involve creating a variable, whether global or an instance one for the player. Have it be 0 at runtime at first and add +1 every the player makes an action (such as moves onto a tile, uses an item, attacks, etc), and then check if = 3 each turn after, and fulfill the conditions to ignore actions if true. I'm not sure of the logistics there in exact, that's the problem. There's a basic idea. I'll try to make you an example later when I get time. You could set an instance boolean for the player (usedupturns=false) and set it true when their turn limit hits 3, and then run the eventing for the enemies. Rinse and repeat.