does potassium migrate down into soil
My high school softball field's MSU soil test indicated potassium required and I have read that potassium doesn't migrate down into the soil and pretty well stays where it's put. I don't understand how the potassium will get to the roots of the grass if spread on top of the soil.
You are confusing potassium with phosphorous another essential mineral nutrient. Potassium is relatively mobile in the soil and is subject to leaching loss. Potassium will move quickly into the root zone.