I'm not talking about same day registration. If you are on the rolls and proof of citizenship is not required to register, then how do you as a poll worker know the person on the rolls is a citizen?

You don't, but also you don't have to. Voter rolls are cross referenced with other sources of data to verify citizenship. ID is required to submit a non-provisional ballot even during early voting if you're not in your designated precinct.

Also just generally it's a severe federal crime to vote illegally, so people who are here illegally aren't out en masse publicly tying their identity to federal felonies.