Some stations do require you pay on-site, and it's not necessarily the only tax. When I flew out of PTY, I had to make a separate departure tax payment as well as some of the other taxes (not nearly as much) that came out of my paycheck.

Was that DX tax the only tax you were charged? If not, you may be right about it being a double charge. I would contact United refunds department and ask them to look into it.