On-hit effects inherited by Doomed Shadows?

[The Tapir]

So on my current Doomed run, I decided to max Shadows and see how far a new build could get when I noticed something that seemed a bit odd: my shadows seem to be inheriting the 10% on-hit chance of Call Lightning from the Eel-skin armor I have equipped. Now, I can't say for certain that this is true, but I swear I've seen lightning bolts strike enemies that looked as if they originated from a shadow. Is this supposed to be happening? If so, are there ways to build a Doomed around stacking on-hit effects from gear and weapons and only investing in Shadow Warriors?

[HousePet]

Isn't that 10% chance of Call Lightning on Wild Gift though? I don't think they get wild gifts.
I also can't see anything that would cause Shadows to inherit anything from their summoner, or any way they could be using Shadow Lightning with you having Shadow Mages. (unless there is some sort of funky difficulty scaling mess up, check their talent list.)

I can however see a bug that stops them getting their bonus spellpower from Shadow Mages.

[The Tapir]

Idk if the lightning is part of the wild gifts category or not, but I'm still seeing lightning strikes from the shadows occasionally when they melee. It might be a visual glitch or some other effect that happens to look like lightning, but for all I can tell they're getting extra damage from the procs. I'll see if I can get some conclusive evidence as to whether or not it's actually happening or not.

EDIT: Turns out I forgot that the shadow mages skill gives them the ability to use shadow lightning. No on hit effects are inherited.