Immigrant as a U.S. State Governor? Has this ever happened before?

Alabama
Robert Burns Lindsay, Governor Alabama 1870-1872, Dumfriesshire, Scotland

Florida
Ossian B. Hart, Governor Florida 1873-1874, born near what became Jacksonville, Spanish territory of East Florida - on January 17, 1821, one month before it became US territory under the Adams-Onís Treaty of 1819.

Georgia
Button Gwinnett, Governor (actually President of Council of Safety) Georgia 1776-1777, England
John A. Treutlen, Governor Georgia 1777-1778, Kürnbach, Germany*
George Handley, Governor Georgia 1788-1789, England
Edward Telfair, Governor Georgia 1789-1793, Scotland
James Jackson, Governor Georgia 1798-1801, England
David Brydie Mitchell, Governor Georgia 1809-1813, 1817-1820, Scotland

Mississippi - none that I could find.

*For a second I thought we might have an Austrian precursor in Treutlen, as one site lists his birthplace as Austria. Best I can tell, Kürnbach was in Würtemburg at the time (1734), which was not part of Austria.

Tennessee - none that I could find

It’s not necessary to count foreign-born people who were citizens of a state when it became part of the United States. U.S. law declared all such people to be natural born citizens of the United States.