Say a Canadian visitor buys in Michigan, sleeps in Ohio and goes home through New York. My guess is the Michigan ticket stays under Michigan claim rules, not wherever the player lives later. Is that the simple way to think about it?
Your simple reading is correct: a ticket sold by the Michigan Lottery is a Michigan ticket even after the buyer drives into Ohio, New York or Canada. Powerball says prizes must be claimed in the jurisdiction where the winning ticket was purchased.
Michigan's rules therefore control validation, deadlines, claim locations and required documents. The winner's country of residence can still affect identification, US federal withholding and home-country tax reporting, but it does not move the ticket into a different lottery's claim system.