gklop, Tilapia will stir up the bottom, but more from nesting than foraging. Tilapia will suck in detritus, filter out and chew what is edible, pitting out what isn't. If your pond clears naturally, I've never seen the Tilapia "muddy" the water very much at all.
The Tilapia will also pump oxygenated water into the leaves on the bottom to help aerobic bacteria break the leaves down faster. Tilapia like the bacteria more than the leaf litter.
As for the brown color...I have seen a lot of ponds this year that have brown algae growth rather than green planktonic growth.
When you used alum in your jar test, did the floc float before sinking? If so, it was an algae or other organic life, and not clay or inorganic solids.
