Entry with a tourist visa counts as an admission. Any entry with inspection at a border or equivalent (e.g., at an airport) counts as an admission, even if the person enters with false documents. The only exception is that a person who entered falsely claiming to be a U.S. citizen has not been "admitted." The immigration authorities can deport someone who has overstayed a tourist visa, since he has no right to continue to be present in the United States.