According to the wiki, oligarchs will offer you a job only after becoming a gladiator and defeating your first gladiator enemy in the Arena.
I only won 2 arena fights (rathounds and psi bettles) and yet all of them are offering me a job already. The oldest save I have is the autosave from before the rathound fight, I will check if one fight is enough as well.
I'm not even sure if this is a bug, maybe the information on the wiki is simply incorrect.
