I assume it's being used literally, rather than metaphorically, here.
Even if ...
Shouldnt he say just Diaboli?
I dont speak latin ... but those words simply dont fit the scene.

You are assuming a modern translation: advocatus = advocate = lawyer. A more accurate translation of "advacatus" would be agent.
Wyll thinks she is Zariel's agent. He might even be right, given the misdirection and half-truths we have been told about the origin characters.