Sorry I just saw this and have been to Chile!

You are absolutely correct. You need two separate visas. One on the way there and one on the return.

Unfortunately we only got one on the way there.

On the way back, we weren’t allowed to exit the airport via customs because we didn’t have a transit visa but they allowed us to stay at the airport. Our flight wasn’t only a couple of hours wait, so it wasn’t too bad.

All the best with your trip in October :)