Wishing, just to make sure, a Tactic per se doesn’t trigger but a tactic with a Move will trigger? So it’s the Move that triggers?
Yeah, basically, but I would try and not focus so much on the word "Move". Instead, focus on the word "Action".
A tactic is not an action, so normally they cannot trigger anything that triggers off an action. But Maneuver is a special case, because the rules for that say "You may declare a standard Move Action with a friendly gladiator model at no fatigue cost."
Maneuver can trigger a reaction despite being a tactic because it literally says that a model declares an action (and then resolves it). The word "action" means reactions work. None of the other tactics cause actions to happen, therefore you cannot react to them.
And the reason you cannot react to repositions and disengages is that they are not actions.