Yeah, the terminology can be a bit tricky. After you activate your creature, it has been activated and remains so until it's done acting. This whole time period in which it is active is called both its activation and its action phase.
Exid is completely correct that the condition falls off at the end of the creature's activation, i.e. the end of its action phase. Which is NOT immediately after it has been activated. This will happen regardless of what actions the creature actually takes. A common tactic is to just guard with the creature, because then you will still get to use its attack in the form of a counterstrike. If we're talking about a Mage, you will want to wait until after your action phase before quickcasting any attack spells, so that the Daze doesn't affect the attack spell.
If it helps, the terms can be loosely described as thus:
Activate = (verb) Describes flipping the creature's action marker. This is the first part of a creature's action phase.
Activated = (verb/adjective) Describes a creature whose action marker has been flipped and is now in their action phase.
Activation = (noun) Describes the entire process of flipping the action marker AND acting with the creature, making it synonymous with the creature's Action Phase (and less confusing if you just say Action Phase).
