So the Rougarou will move AFTER taking 1 damage per investigator. Does this happen the instant he takes 2 damage (assuming 2 investigators) - or does all the damage get added to the Rougarou in the phase, then, if that total is more than 2, he moves?

Any ideas? Am I overthinking this

I'm thinking it's the former, as it's an after effect, which happens instantly the condition is met ?

You're overthinking. Just do what the card says.

He moves after taking 1x Investigator number damage in one phase. After that amount has been taken, he moves.

Damage is applied instantly. (You can shotgun him in the face 5 dmg) and then he will move.