This is from Time's 100
Tenzing: May 1914, in Solo Khumbu, Nepal; Hillary: July 20, 1919, in Auckland, New Zealand"
"Tenzing's birth may have been humble, as Ullman says, but it also had lucky portents. His parents lived in the high mountain village of Thame in Nepal, but at the time of his birth, his mother was on pilgrimage to a holy place called Ghang Lha in eastern Nepal." In this case, even his own family is saying he was born in Nepal
So he is in fact Nepalese. I have heard that Tibet and Bhutan have claimed Tenzing as one of their own, but this is without foundation, especially seeing as his parents were Nepalese, and he was born in Nepal (as shown above).
Also a Sherpa, is a native of the region of Nepal which is around Everest. They originally migrated from Tibet hundreds of years ago, and although Tibet claims to have Sherpa's they aren't Sherpa's in the true meaning of the word.
Also on Edmund Hillary, before joining the NZ Air Force, he was a beekeeper (as was his father).