Whirlpool bath systems are installed on bathtubs so that when filled, the system and pump fill with water. Therefore when the water is drained from the tub, the system and pump drain as well. Also if you've noticed, the jets are probably at different heights, with the lowest jets usually near the drain. Buy U.L. code each jet is allowed a couple of onuces or less of water.
It sounds though that this system is trapping water somewhere in the series of pipes (sagging pipe, maybe). One way to verify this is to turn the pump on without any water in the tub, just for around 5 seconds. (Don't worry you won't damage the pump seals) If water comes out of the jets, the system traps water and needs to be repaired by a service person who specializes in whirlpool bath systems. If no water comes from the jets, 2 cups of cascade dishwashing powder in bath water as hot as you can get it for 10 min. seems to work. However a whirlpool maintence cleaner like Whirlclean should be applied 2 times a month.