Reporting part-time earnings while on benefits - 7 months and counting

I picked up part-time shifts as an operations analyst and I am confused about how to report them. I would rather hear the honest version than the polite one. Sometimes my paycheck is late by a week. Do you report when you earned it or when you were paid?

I estimated and then checked my pay stub. When there was a small difference I wrote to the agency to correct it.