There are many threads here about why you should never dump a partially full black tank. The short answer is that it takes a long time to break down solids and paper. They have a tendency to "stick" to the floor and walls of the tank; especially directly under the hopper. The drop point is also in the vicinity of the wall sensors in most installations and paper drooping on the sensor heads is the most likely cause of false tank readings.
Calgon water softener added before you use the tank is supposed to limit the sticking of solids to the bottom and sides of the tank. (My experience with this is positive)
You need a "large volume" of water to sweep that crud out of the tank along with any undissolved paper. The corporate knowledge is to fill the tank till at least the full light comes on (about 2/3 full) before you actually pull the handle to ensure a complete dump.
The flush/rinse system on most installations just shoots water at the wall opposite the sensors. It is located at the top of the tank and most likely will not do much to clean your top sensors or loosen stuck crud unless you let it fill the tank a couple of times.
Photo of black tank and location of white "turboflush" line can be seen in this photo:
Lou and Laura with Bella - German Short Hair Pointer
2008 GMC Sierra 2500HD Crewcab SB Allison Duramax
2010 Flagstaff 8526RLWS - Superglide 3300
HAM CALLSIGN - KC3FFW