Right. Doesn't that make him British? Asking honestly... How could he have been American if the USA didn't exist yet. Obviously he was North American, but his citizenship at birth would have been British, no?

When the area you were born or live in changes governments, does that make you an immigrant?

It's in the Constitution: "No Person except a natural born Citizen, or a Citizen of the United States, at the time of the Adoption of this Constitution, shall be eligible to the Office of President". - Article II, Section 1, Paragraph 5

As you can see, this covers the corner case you've identified.

Interestingly, the term citizen wasn't defined until the 14th amendment: "All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside"