The test does not involve a 'surge'. The trip mechanism is generally a one-shot disconnect, as you'll see from post #7, so triggering the device is not helpful!This simply injects a surge and check when the SPD trips and shows you the trip V. Then you can check if the trip V is the same as the one that the SPD manufacturer gave you in the datasheet.
The test involves slowly ramping up the applied voltage (from a high impedance source), and measures the voltage at which the MOV begins to conduct, as you describe. That doesn't harm the SPD as the current involved is small.