Well, I don't read the instructions very well. Because I would lightly rinse the surface to remove all the residue after I have determined that the area was clean and void of all mold, mildew and dirt.
Now, here is a simple test. With clean hands, wipe them across the surface of the walls and IF powdery or chalky substance rubs off the walls onto your hands, I would not apply paint to that surface. I would want it completely void of residue.
The old TSP was nothing but strong Spic and Span, which would turn your hands red if you did not use long gloves. The new stuff is not that un friendly at all and I have not used it since. I will use bleach and scouring powder.