When in lane and pushed up to the enemy, I used my Cutthroat to teleport to a Zilean bot just to test my mobility since the E is a "teleport" that does no damage but only amplifies damage AFTERWARDS.
Instead of just teleporting, however, the turret identified Cutthroat as a damage ability and switched aggro to me even though I had not attacked Zilean and still had my ally minions in the turret range.
As far as I know abilities under turret that simply silence, stun, slow, fear without doing any damage will NOT draw aggro (Ex. Fiddle fear under enemy turret is a great once I enjoy using).
Steps to reproduce:
1) Push minions to turret
2) Have a few ally minions with you attacking turret
3) Cutthroat to enemy and do not deal any damage
4) Die from turret aggro :(