bathroom sink, and possibly the washer drain into one tank. sounds like that's what you have.
my routine is to drain the black tank, then use the san-e-flush to rinse. i have a clear plastic elbow on my dump fitting so i can see when things run clean. after rinsing the black for awhile, i close the black handle with the san-e-flush running for about 2 minutes, then i open the black valve and let it run until it looks clear, stop the san-e-flush, and when flow stops, close the valve. i assume you could then do the rear black tank. finish by emptying the grey tanks to flush the drain 