You haven't done anything wrong, this is an issue with minecrafts UV mapping and the atlas system conflicting, causing some texture "leak".
I had this same issue on this model here.

To fix this issue I had to create new 4 new textures of solid colors and then select each element and set it to that specific color.

With this done it greatly reduces the texture leaking.
After this i started making palettes and I haven't had any issues since then.