You need to enable the glossiness in paint mode. Its the little ball at the top next to your green ball at the top. The three are depth, opacity, and glossiness. You can see in your picture that the glossiness has a X over it. That signifies that it is not being used when you paint or apply the texture. It's the little area in pink in my attached picture.
Okay I think I get it. What you want to do is just import a mesh for texture painting. That is why you choose "Paint UV Mapped Mesh (Per Pixel)" in the Start Menu Popup. First make sure there are no subdivisions in "Initial Subdivision". And there is a checkbox for triangulate. Make sure it is not checked. There are a few other options concerning your smoothing, and UV's but this should take care of the additional triangle problem you have been having. I have also attached an obj file made in blender. Here are the settings I did for it so you can see. Normal Map Software Preset = Blender (Only because its what I used to model in) Initial Subdivision = No Subdivision (Will mess up the mesh) UV Map Typing = Keep UV (Note this is just because I have a UV set already on the two meshes) UV Set Smoothing = Smooth, Keep Edges (May or may not apply to your mesh) Nothing checked below except "Lock Normals" (Make sure "Triangulate" is not checked) untitled.obj untitled.mtl