Does the cool-down of the Invisible Fist monk alternate class features start when the ability begins, or when it ends?

Invisible Fist is a fantastic pair of monk alternate class features, and a pretty good justification for taking 9 levels of monk in a ninja-like character. Both activate as an immediate action, and have the clause “You must wait 3 rounds before you can use this ability again”.

But are these 3 rounds counted from the activation of the ability, or is it 3 rounds from when the ability deactivates?

I think it would be the former, since you “use” the ability as an immediate action to activate it, but I would like to know if there is some precedent going one way or the other.

This is most relevant for the blink ability, because if your Wisdom is 16 or higher you could have a permanent blink effect by overlapping the durations, but it’s important to know for the 1-round invisibility ability, too.