Mediates the conversion of geranyl diphosphate into alpha-terpineol, a monoterpenol. Monoterpenols contribute to the final grape and wine aroma and flavor. Also forms some 1,8-cineole and traces of other monoterpenoids. (2E)-geranyl diphosphate + H2O = (S)-alpha-terpineol + diphosphate Binds 3 Mg(2+) ions per subunit. Secondary metabolite biosynthesis; terpenoid biosynthesis. The Asp-Asp-Xaa-Xaa-Asp/Glu (DDXXD/E) motif is important for the catalytic activity, presumably through binding to Mg(2+). Belongs to the terpene synthase family.