When painting onto a face with a multi-pixel tool, the paint gets onto other faces:
The texture UVs were created with the atlas function, so different faces shouldn't be sharing textures. The problem is that the program doesn't distinguish between pixels that are on the face, and pixels that aren't.
This gets into my way of painting with the brush and paint bucket tools, as I basically can't use them at all without messing my entire model up. It's not fun being restricted to just pencil tool, either.
A fix could be to check if the pixel is in the face's UV before modifying it.