I am waiting to install my Tornado. I would dump the black. Than with leaving the black valve open use the Tornado for approx 2 minutes (as per instructions that came with it). Once the black is clean I would keep the black valve closed and empty the gray.
I have a 45 degree clear piece added between my sewer hose and the trailer connection. With this you can see if you are running clean or if another blast with the Tornado is necessary.
I think that I will be only attaching the dedicated tornado hose when dumping. When not attached I will connect it to my spray nozzle. I am paranoid with the fact that if someone was to turn it on while I was away an awful surprise would be in store upon my return.
I have witnessed the result of a friends black tank filling up from a faulty toilet flush valve. Stinky water was coming out of everywhere. That just scares me.