I will join in on those asking for a bit more clarification on the whole freshwater filling up the sink and overflowing to the black tank. Could you tell us EXACTLY what you are observing?
I had a plastic toilet in a TT once that was leaking internally into the black tank, not through the bowl so you couldn't see it happening. Just a thought. In that somewhat rare instance, the black could fill completely up to the flush valve which would be closed and in good working order. Since the water would have nowhere to go, it could climb the sink drain if you have one that is plumbed to the black tank.
That is all a lot of speculation on my part to try and make sense of a confusing situation as reported.