Correct; the oxide is not a problem. There's not much of it, it melts at a much higher temperature than the pure metal, and it floats, so you just scoop it off before you pour.

Whether oxidation or reduction is taking place during the melting process is determined by the amount of oxygen arriving via the air blast; too much oxygen and you get a hot oxidizing atmosphere, which oxidizes both my iron crucible and the top of the melt. Too little oxygen and you can actually get a reducing atmosphere, the furnace runs a bit colder, less heat escapes through the flue. So it's a tricky balance to strike and I'm still fine-tuning it.

I add potassium chloride and sodium carbonate to flux the melt and remove dissolved hydrogen; the KCl helps keep more aluminum oxide from forming apparently, though some home foundry sites report that they don't see a difference if they skip that step. Both chemicals are cheap, so I'm not too concerned.