The water supply to the unit will come from your home water supply...it will then pass through many stages to remove the impurities...the DI portion is probably the most important for aquariums as it removes the positive and negative ions from the source. Some of the negatively charged ions, (phosphates, silicates, and nitrates) are removed here...these most strive to keep out of the tank.
End result is usually a 99% pure water source.
To answer your question in the shorts...no you do not filter the tank water already in the tank through it...you make new, virtually pure water...make some coffee with this water...you will be amazed at the taste difference.