Reporting part-time earnings while on benefits after 5 years as a hotel front-desk agent

I picked up part-time shifts as a hotel front-desk agent and I am confused about how to report them. It has been a long 3 weeks. Sometimes my paycheck is late by a week. Do you report when you earned it or when you were paid?

The claimant handbook has worked examples for part-time pay. Mine was clearer than the phone line.