Since the Trolls say "when x engages a player sack" does that mean the troll doesn't sack when it is voluntarily engaged by a player or from Hungry troll?

Tom: "After Tom engages a player, sack 1".

It sacks you regardless of whether you choose to engage it or it engages by itself. In both instances the result is that the troll engages you, so Sack 1 happens.