Based off this video by @flightx3aa, I tested the O.M. shield for the pets.
For the sake of my sanity, I only tested this for Gunslinger. The pet only gets the bonus if they are standing in the ring while attacking, so for melee pets you would need to drop the ring on top of the enemy they are attacking and hope they stay inside. Good luck with that.
Anyway, first things first. This was a massive pain in the ass to use. The pet moves a lot passively, and the ring isn’t big. It will frequently move out of the ring because…reasons I guess. I tested on Mayhem 0 with this spec. Gunslinger’s normal attacks with the SMG do get boosted (went from 502 to 743 or so), however the attack command receives no bonus from 0.M. Don’t ask me why, I have no idea. Just enjoy the spaghetti.
Overall it’s a nice find, but for pet FL4K’s I’d rate this in the same tier as the ele-crit nova anoint: fun in concept and thankful for SOMETHING outside the normal damage formula, but so impractical that it just isn’t worth incorporating into your build (I don’t mean the anointment doesn’t work in general, I mean it’s a pain for pet FL4Ks. Yes, they can proc that anoint and no, you don’t want to test it).