The UVs are looking really weird. Have you UVd the high poly mesh from Mudbox? On top of that they seem very distorted in certain areas, you probably have applied some kind of auto mapping. I'd say the model you imported into Painter isn't at all ready to be painted on. You need to retopologize your model from Mudbox, create new UVs for that new low res model, and import that into Painter.
You also need to assign materials with unique names to your object (like e.g. a phong material named 'Eyes' for the eyes). Those names will be displayed in the TextureSet List in Painter. The TextureSet 'phong1' might be the eyes, who knows. Try to select it and check if you can paint on the eyes.