It seems that readers are supposed to have the intuition of this meta-rule. As far as I know, this is not said directly anywhere, but rather seems to be simply an element of the underlying structure of the game that has never deserved a direct explanation. Fortunately, the game provides at least a similar clear example that demonstrates that the rule is true.
Dragon's blast weapons can have various effects, but a dragon must usually wait 1d4 rounds before using the blast weapon again. the Draconomicon on the rules: Breath Weapons says
The weapon of the breath of a dragon is a supernatural ability. It does not work in the anti-aggression areas. The use of a breathing weapon is a standard action. As indicated in Manuel Monsterwhen a dragon uses a breathing weapon, he must wait 1d4 rounds before he can breathe again. In this case, the turn lasts until the beginning of the next turn of the dragon (see The Fighting Round, page 138 of the Player's manual). For example, if a dragon breathes in the first round of combat and the die roll so that the weapon of the breath can then be used is equal to 1, the dragon can breathe again on turn 2. If the die is a 4, the dragon could not breathe before the fifth round. (22 and link added)
This covers all breathing weapons, including breathing weapons of a duration similar to that of the smoke drake:
As a standard action once every 1d4 rounds, a smoke drake can breathe a cloud of cloudy smoke over a 30-foot radius that conceals (20% missed chance) all creatures that are inside. Thanks to his blindsense, the duck ignores this missed opportunity. The mist lasts 1 minute … (157)
So when the alternative class function invisible fist says: "As an immediate action, you can become invisible for 1 round. You have to wait 3 rounds before you can use this ability again" (Examples of evil 21), this means that, like a dragon's breath weapon, the monk could, in turn 1, take immediate action to activate the invisible fist. The monk can not reactivate the ability this turn, turn 2, or turn 3, but may turn it back on turn 4 or later. And, to be clear, it would be invisible from the count of initiatives during the ability has been activated and until just before this same initiative relies on turn 2. (Adjust the exact moment when the ability can be reactivated appropriately if the monk activated the ability while it was not his turn.)
The invisible fist alternative class function continues saying: "At the 9th level, as immediate action, you can use wink, as a spell, for a number of turns equal to your wisdom modifier (minimum 1 round). You must wait 3 turns before you can use this ability again "(ibid. and link added). Therefore, the monk of turn 1 in turn can take immediate action to activate the invisible fist in order to win a wink The effect continues until the second turn (but not until the end), but if its wisdom score is 14, it continues until the last turn (without going through the turn 3). If his wisdom score is 16, he continues until the last turn (without going through turn 4). The wisdom score is 18, it continues until the (5) round (5), and so on. However, the monk can not reactivate the ability before the 4th turn. wink the effects are probably covered by the same effect rules more than once for different forces (PH 172), the longest duration wink effect of replacing the shorter one.)
Note: Other non-monk class features available at character levels 9 and above lead this reader to wildly speculate that may have thought that waiting periods worked differently, perhaps thinking that waiting periods were measured from the expiry of the duration of one's ability instead of one's activation. That is to say, benefit continually of an effect like the wink to spell is a pretty serious buff – a few classes in addition to warlock receive a continued A third level spell equivalent very early, but the mix of abilities shadows is just as impressive, if not more, and this ability was available at level 7. Really, as a good thing for the monks, this submarine sees no reason to put the special skill in value. invisible fist, even if it's something as boring as a continuous wink effect.