Emergency Stop switches are normally closed, and go open-circuit when mechanically tripped. They are normally-closed to confirm the wiring and switch are there, and that there are no faults with it.
The spa should have a start/stop switch which is activating a latching relay, which may be the pump contactor+side switch.
The E-stop would be wired in series with the latching relay/contactor coil circuit and de-energize it once the E-stop contact goes open-circuit due to being pressed.
It should not just start the pump back up if you reset the E-stop. You need to press Start. So it typically latches off.
If the motor overload or low water tripped it should latch off and not just start back up again, you would get a pump going on/off/on/off etc.
There is a danger if the E-stop is not properly waterproof as it likely has mains voltage present, and wet hands would not be welcome hitting it.
I don't know your particular safety standard, but common sense also helps.
Had a nice bird get a bun cheek stuck on the suction vent, by time the pump was switched off she had quite the welt lol. Who'd have thought of the dangers of the spa?