Doesn’t look like you had uploaded the image, but from what I remember, it sounds like it is working correctly.
When you are exporting the PSD file, you aren’t exporting the entire model. The image that you see when you open up the PSD file is based on how you had the model set up in the Sculptris viewport.
There are many reasons to use the PSD export, but one of the most common is going to be in using photos to texture your model. Once you’ve saved it back out in PS and import that file back into Sculptris, the program basically projection maps that texture onto your sculpt. You could also do all of the texture painting directly in PS with some slightly differing results considering all of the brushes and options for brushes that you have within PS (also good for having a way to perfectly match a color given multiple models).
When you see the model split into the dark and light parts, that is due to symmetry being on. Anything that you paint onto the light side will be duplicated on the dark side once you import it back into Sculptris.
If you are looking to just paint over an image of the sculpture, go to “OPTIONS” which is just under the detail slider. At the top right is “Save Image”. I usually turn off “Save with BG”, but turn on “Save with AA”. That just turns off the background and makes it black as well as turning on the anti-aliasing so the edges of the model are a lot crisper. You can then open that file to do a paint over in PS if that was what you were attempting to do.
Hope that helped at least a little.