You can find a listing of Union generals here.
By my count, of some 550 Union generals, roughly 20% were Southern-born.
Of those, about 1/3 came from Kentucky, followed (in descending order) by Virginia, Maryland, Washington DC, Tennessee, Alabama, and the Carolinas.
Even Georgia, Florida & Delaware each contributed one or two Union generals.
I could find no record of Union generals born in Mississippi, Louisiana or Texas.
Nor have seen reports of a Confederate general (out of 400 appointed) born outside the Confederacy.
Of Union generals, perhaps 10% were born in other countries, especially Prussia.
George Meade, the victor at Gettysburg, was interestingly born in Cadiz, Spain, son of a Philadelphia merchant naval agent for the US government.
After his father's death in 1828, Meade's family returned and lived in the South, where he also spent most of his civilian and military careers.
There were a few, not many. Two that come to mind are Samuel Cooper, who was a full general in the Confederate army and served as Adjutant General for the duration of the war. He was born in New York. And Josiah Gorgas was the head of the Confederate Ordinance department and promoted brigadier general in the later half of the war. He was from Pennsylvania.
I don't think you looked very hard.
Pemberton, the loser at Vicksburg, was born in Philly.
There were others, notably Patrick Cleburne, who was born in Ireland.