Does Heimerdinger also apply this on-hit effect with his wrenches?
No. It's an effect solely unique to the turret. Same with the slow from his ultimate and from Zyra's E plant.
I went into a custom game to test this under a few conditions. The turrets(Shaco, Heimer, Zyra) deal basic attack damage based on the ap and skill level of the champion who created them. The point being that the damage source from the units is their basic attack. This is where ninja tabi is in question. Since the damage source from these units is their basic attack, this item should reduce their damage.