The mediator doesn't really affect the compatibility of your programs. How does it work ?...
You will need a video card (Voodoo, Virge...) which means at least that your Amiga will have 2 outputs for the video :
- the standard output (on the motherboard)
- the video card output (from the Voodoo or Virge card)
Following your applications are compiled for runing under WB or not, the output signal will commute to the right video output.
Usually, old demos & old games will always ouput put to the standard output. And application under WB will output to the WB screen resolution : the video card output.
So now, you can guess the problem is not what you first thought :-?
Either you have 2 screens for each of the 2 outputs, or you have only one screen (multisynch or not) providing 2 inputs (plus one Scandoubler if no multisynch screen)