the /skin set player command could use the wrong model, if you are in offline mode.

Humm, this is strange, since API used is the same. Could you tell the player you were testing it with?

/skin set player Emhl (it's my own account)

Oh, I read it wrong ... Wdym by could use the wrong model? Model doesn't depend on the status of the server. It depends on skin model saved in mojang skin DB.

I use the slim model for my skin. but /skin set player Emhl always displays it with the classic model.

I think it's a problem with ely.by API. There's probably an account with same name there. You could try contacting them, as their TOS (rule 5) means that you can request to restore your username.

Alternatively, you can do

/skin set URL slim http://textures.minecraft.net/texture/ba31432c44cb9db77a58c6a4d78555180fb3dbd73353320d5bf95f28bec86704