I installed this mod on server side and client side both.
This happened on a server.
When there are two kinds of skins in this server, layered and not layered, this mod treats players' skins in the same way no matter the skins are layered or not.
Problem occurs when layered players watch not layered players or in reverse.
I don't really know if this mod cause the problem.
So if you need more details, feel free to contact me.

Please check if mod is correctly installed on the server side, it might be corrupted.
Those skin layers in a multiplayer server is the only feature that need the mod to be installed on the server.
If the mod file on the server side is functioning correctly, you should see those layers on other players that have skins with layers, unless they have them turned off.

Lastly, I no longer offer support for this mod, 1.7.10 is very old, sorry.
Please consider move on from 1.7.10.