He should absolutely report when he moves so that he continues to receive his paperwork timely. They’ll want to know about any changes to expenses, and when he indicates the rent amount, they’ll want to know how he’s paying or how he’s going to pay. He can explain then that he’ll be doing under-the-table work seasonally and they should advise of what they’ll need from him to verify it.

But, strictly speaking, he doesn’t have to report the income for SNAP until his next renewal or SAR—the only thing required to be reported for SNAP in PA is income exceeding 130% of the FPIGs, which would be $1,473 for your cousin, and based on what you said he won’t earn that much.

For Medicaid, it’s any increase in income of $125/mo or more, to be reported by the 10th day following the month in which the income begins. Which doesn’t actually matter right now because everyone’s Medicaid in Pennsylvania will go to their next renewal after the COVID-19 PHE ends.

Edited to add: As someone else noted, your cousin can report changes via COMPASS if he knows his case record number. Or he can call the statewide customer service center at 1-877-395-8930.