I primed the pump and everything ran fine. When I shut the pump off I could hear the filter immediately start to drain water.
If your system ran fine with no water leaks and then drains when you shut the pump off, you almost surely have a suction side leak. Somewhere between the pump and the skimmer, air is being drawn into the system.
When the pump is on, that air is manifested by all the bubbles you see in your pump strainer basket which then travel into the filter. When the pump is shut off, that pressurized air forces all the water back towards the skimmer.....that's the sound you hear.
Even after the air in the filter is unpressurized, air continues to leak into the system and, eventually, all the water is drained back into the pool.
The cure is to find that leak. The most common place is the strainer basket lid where the o-ring doesn't seat properly. Next, you could check carefully at all the suction side valves.....they leak frequently. Also check the drain plug(s) at the bottom of the pump strainer basket.
Once you find that leak (or leaks), your system will stay primed.