I haven't used ADA substrate, but I have set up a couple of tanks without bothering to wash the substrate, and managed to avoid any sort of cloudy water.
I typically do the setup - putting in substrate, planting plants, etc., and periodically mist it with a sprayer bottle full of water.
Once I'm done, I generally fill the tank by pouring the water onto a chunk of spare sponge or something.
I suspect that the misting is washing the fines down into the lower layers of the substrate, and out of the way of currents, etc.
But I don't think I can really validate/verify that. All I can really say is that this is what I've done on a couple tanks, and have had seemingly good results.
Although, my experiences are mostly with setting up new tanks, I imagine you could get similar results if you drained a current tank down below the substrate (stick in a chunk of pipe or something to avoid drawing up substrate)., misted it heavily, and slowly added water.