The "sink" part baffles me.
As for fresh water filling up the black tank, I had this happen once, and I believe I was using the "city fill" inlet with a hose connected to my house, and I think I the pump was also on, and I put the valve control in my wetbay to "Fill Tank".
Somewhere in that combination, bad things happened...and my black tank filled.
I'd check to see what your valves are set to. As mentioned above, the water pump ONLY turns on if there's low pressure on the outlet side of the pump. You should be able to leave the pump on all the time, and it should only come on when you open a faucet or flush.
Jim