I do not know about the Aqua King PREMIUM but we have the Aqua King 3.8 GPM pump that feeds into a Shurflo accumulator tank. Have had it for years and it works perfectly.
My understanding is the accumulator tank keeps the pump for cycling on/off rapidly when using the water
. In our system, with the tank at 40 psi, we can draw about a cup of water
without the pump coming on. After that, the pump runs steadily until we shut the tap.