I'll take my stab at this.
Following the title you are trying to rinse out your black tank(s).
Your post says you have two unmarked connections. I'm guessing for water hose hook-up to rinse the tank(s).
This is the hard part because every brand, model, year of trailer can be different. In my wet bay there are 3 places to hook up a water hose. A city water connection that goes straight into the water lines. An onboard water tank hook-up that fills my onboard fresh water tank. And a black tank flush hook-up.
My guess is that the one you are hooking up to that is not then running out of your black tank is filling your onboard fresh water tank.