Are 'when an enemy engages...' effects (as in The Ring Goes South) triggered when players optional engage those enemies?

Whenever an enemy moves from the state "not engaged with player X" to "engaged with player X", that enemy has engaged player X and player X has engaged the enemy.

I played it that way and got pounded by location damage effects... Still won, though, so I shouldn't complain.

The Balrog in the next campaign quest is just brutal and not fun at all.