There's no slot for them to equip a soul crystal so they probably just stay as a class. The Jobs are supposed to be about being the special chosen one, it'd be kinda weird if you were the Azure Dragoon and both your Retainers were also the Azure Dragoon.

Unless your retainers are your fellow triplets and you're all running an elaborate scam on Ishgard.

My sympathies to all those Arcanist Retainers who will never become Summoners no matter how many times they beat up Ifrit, though.