Hi, as you probably know the pump and the heater can't (shouldn't) run simultaneously, but I'm not sure that would pop the GFI. AFAIK the GFI just protects against grounding (I think the basic logic is that it compares the current on the line vs the neutral, and if it doesn't match, that means the current is being bled off to the ground, when the GFI detects that, it shuts the circuit off, since the "ground" could well involve a person).
The Watkins GFI might also have a circuit breaker in case the amperage exceeds 20 amps, I'm not sure? But regardless, you probably need to figure out which scenario is happening: draw exceeding 20 amps, current bleeding off to the ground or a bad GFI.
What I would do if I were you, is to open up the control panel, turn on the jets and use a non contact voltage tester ($10-20 at Home Depot or Amazon - it's a great tool to have) to see if the heater and jet pump are both on simultaneously. If thats the case, then it's probably safe to say that theres a problem with the control panel and you are drawing too much current.
You could also just unplug the heater, run the jets, and see if that solves the problem. If it does, then either the heater has an issue, or like you first suggested, the jet pump and heater are running simultaneously. But if the GFI still pops when the heater is unplugged, then you know it's probably the GFI or the jet pump itself.
You could test the current draw as well, but it looks like kill-a-watts only go up to 15 amps, so you'd need a clamp meter and a 20 amp line splitter (which you can make pretty easily if you have a short 20 amp cable you can take apart), but if you don't have that gear, it'd be cheaper just to get a new GFI.
Rob