When I did my bars on my 08 FLHT, the turns did what you described. If I remember correctly, the wires for right and left were either the same color, or very similar. Reversed them, and voila! they now work correctly. worth checking out, as it is very easy to miss.Good luck.

 

Some times no matter how careful we are we get things backwards. It can happen to the best of us.
From what you have posted i would take the time and recheck all connections. I am convinced you have the turns backwards.
Always double check every thing when it comes to wiring. I have a simple method that I use: tape with numbers on it. I just add one to each end of the wiring connection. If I have enough colored tape I prefer to use that. Just match the colors. If not I use painters tape and add a number to each end.

 

I'm betting that the connections are right, he just needs to take the indicator light panel out & reverse it. Think about it, that panel will go into the holder either way, the center light is neutral so it's right, the first ones to the right & left are high beam & oil, so if when he puts on the high beams the oil light comes on the panel is reversed, same for turn signals. Pull the panel out from the holder & turn it 180* & all will be right with the world.

 

Sounds logical to me. I like analytical thinking.