Alum and aluminum sulfate are the same thing. The pH you show should be okay, but the optimum pH for lowest aluminum solubility is 6.5. That is important because as you add alum, it dissociates to form aluminum hydroxide "floc". The aluminum has to be insoluble for this reacted solid to come out of solution, form the floc, and trap the silt solids with it as it settles. The mud balls you see are the reacted aluminum hydroxide with the silt attached. These will settle to the bottom and act like any other silt particles.
The amount of alum needed is dictated by the unique chemistry of your pond. typical minimum dosages are 30 ppm to start to see the reaction taking place. That might be the 100 lb addition rate your jars show. In that case, every addition you make would be at that rate, regardless of previous additions, since the alum reacted, settled, and is no longer in solution to act to reduce subsequent addition rates.
If you did not see effective results the 1st time, it might have been due to the lime addition boosting the pH too high the 1st time, and the resultant pH after reaction was 7.5. The second addition will further lower pH as it takes OH out of the water. Watch the second addition rate closely for too much pH drop. If it drops below 5.0, you will need addition of more lime. it is a juggling act.

Good luck.
Mike

Mike