Everything between now and the next game is just killing time
You are both correct!
But don't take my word for it, you can read the designer's answer right here!
EDIT: For a counter example see the wording on Stun Bolt
Power: The Wraith deals 1 Target 1 Projectile Damage. Until the start of your next turn, reduce all Damage dealt by that Target by 1.
This card does not specify that the damage needs to be dealt to reduce the target's damage.