Yes you are right, although he wasn't born in the U.S he was Serbian-American
He was Serbian.
Then he became American.
That's it, just American.
Tesla was always a proud Serbian. While he took pride in his American citizenship, he always remained very proud of his heritage. To say he was just American is plain wrong. He was a strong ambassador of Serbian culture in America, even himself translating many 19-th century Serbian works to English.