Pet job means most of your damage comes from your pet or that the pet damage contributes to at least 50% of the damage.
Egi is just a glorified DoT that makes up about 1/3 of overall damage.
I don't think pets work in XIV.
I think they need to overhaul egi's and turn them into different trances and have them summon the summon just like you do with Bahamut and Phoenix.
That delayed pet attack is awful. It's like using a macro'd skill.