I have a very similar workflow, and experience similar temperaments from the agents. I also find anecdotally that they are moderately competitive - you get very different attention from them when you say "competitor X wrote this - please find all bugs" than when you say "you just wrote this - please find all bugs".
Hah yea I just told them I wrote it, or I reviewed it. I don't want to get the AI's in a pissing contest with each other because they will get distracted and try to show off.