I want to say that neither does a Sniper’s Sniper countdown tile, but for sure a Lieutenant’s Pistol countdown tile is not triggering it.
Does that one actually do fixed damage, or is it just the tile destruction damage? If it’s the latter, it shouldn’t trigger Practiced Offense. I know at least one of the Hammer Soldier options just does tile damage for the row destroyed, and that doesn’t trigger it.
@Shiholude
As @TPF_Alexis stated, Practiced Offense will not trigger when a power only destroys tiles.
The Sniper’s Deadly Shot power does deal damage, but that power is a passive power. Passive powers won’t trigger Practiced Offense.