Hi there,
I also have a D620 on what I call the docking station. I think what you might be seeing is the second desktop on the external display. I am seeing the same thing that you are seeing when I tested this out. I don't use it in this way so I never have experienced the issue until now. My setup is either only the built-in display or the external as a second screen.
If it were me, just use both - more screens are better But if that doesn't work for you, try both the VGA and DVI outs on the docking station. I am using the VGA.