I can't provide specific time-lines, but I rather suspect that there wouldn't be much hydrogen left in the area by the time oxygen shows up. Stars don't fuse everything at once. When the initial hydrogen-to-helium2 tapers off, the radiation pressure can't maintain itself against gravity, and the star collapses a bit. That compression allows the helium2 and remaining hydrogen to combine into helium3. The next stage is lithium, then carbon (beryllium and boron are in there too, but not really important). After carbon comes oxygen, by which time pretty much all of the hydrogen is gone. Remember also that at stellar temperatures the substances are in plasma form rather than gaseous, so molecular bonding can't occur. Fusion is the only way that atoms can combine, since all of the electrons are stripped off and flying around loose.