If an ability has a waiting period between uses, that waiting period typically begins immediately after the ability's activated
It seems readers are supposed to intuit this meta-rule. That is, so far as I can tell, it isn't directly stated anywhere but appears, instead, simply to be a piece of the game's underlying structure that never merited direct explanation. Luckily, the game provides at least one clear similar example that demonstrates the rule is true.
The breath weapons of dragons can have a variety of effects but a dragon must typically wait 1d4 rounds before using the breath weapon again. The Draconomicon on Rules: Breath Weapons says
A dragon’s breath weapon is a supernatural ability. It does not work in antimagic areas. Using a breath weapon is a standard action. As noted in the Monster Manual, when a dragon uses a breath weapon, it must wait 1d4 rounds before it can breathe again. In this case, a round lasts until the dragon’s next turn begins (see The Combat Round, page 138 of the Player’s Handbook). For example, if a dragon breathes in the first round of combat, and the die roll for when the breath weapon can next be used is a 1, the dragon can breathe again in round 2. If the die roll is a 4, the dragon could not breathe again until round 5. (22 and link added)
This covers all breath weapons, including breath weapons with a duration like the breath weapon of the smoke drake:
As a standard action once every 1d4 rounds, a smoke drake can breathe a hazy cloud of smoke in a 30-ft.-radius spread that provides concealment (20% miss chance) to all creatures within. Thanks to its blindsense, the drake ignores this miss chance. The haze lasts for 1 minute…. (157)
Thus, when the alternative class feature invisible fist says, "As an immediate action, you can become invisible for 1 round. You must wait 3 rounds before you can use this ability again" (Exemplars of Evil 21), it means that, like a dragon's breath weapon, the monk could, on round 1 on her turn, take an immediate action to activate the ability invisible fist. The monk can't activate the ability again this round, on round 2, or on round 3, but could activate it again on or after round 4. And, just to be clear, she'd be invisible starting on the initiative count during which the the ability was activated and until right before that same initiative count on round 2. (Adjust the precise timing of when the ability can be activated again appropriately if the monk activated the ability when it wasn't her turn.)
The alternative class feature invisible fist continues, saying, "At 9th level, as an immediate action, you can use blink, as the spell, for a number of rounds equal to your Wisdom modifier (minimum 1 round). You must wait 3 rounds before you can use this ability again" (ibid. and link added). Hence, the monk on round 1 on her turn can take an immediate action to activate the ability invisible fist to gain a blink effect that continues until (but not through) round 2, but, if her Wisdom score is 14 it continues until (but not through) round 3, if her Wisdom score is 16 it continues until (but not through) round 4, if her Wisdom score is 18 it continues until (but not through) round 5, and so on. However, the monk can't activate the ability again until round 4. (Overlapping blink effects are likely covered by the rules on Same Effect More than Once in Different Strengths (PH 172), the longer-duration blink effect replacing the shorter.)
Note: Other nonmonk class features available at character level 9 and earlier lead this reader to speculate wildly that the authors of Exemplars may've believed waiting periods worked differently, perhaps believing waiting periods were measured from an ability's duration's expiration instead of its activation. That is, benefiting continuously from an effect like the blink spell is a pretty serious buff—few classes besides warlock get a continuous 3rd-level spell equivalent this early—, but the ability shadow blend is just as impressive if not moreso, and that ability was available at level 7. Really, as a nice thing for monks, this DM sees little reason to nerf the special ability invisible fist, even if it is something as annoying as a continuous blink effect.