How do you report hours that vary week to week? (Tucson)

I picked up part-time shifts as a procurement assistant and I am confused about how to report them. There are 5 people counting on me, so I am trying to be careful. Sometimes my paycheck is late by a week. Did anyone get an overpayment notice from a mistake?

Report honestly and keep your stubs. An honest small error is much easier to fix than a missing report.