There are two types of GFCIs for 240 VAC circuits.
The 3 wire GFCI monitors the current on the two hot wires. If there is an imbalance it trips. It is called a 3 wire device because the circuit uses two hot wires for the 240 VAC and one grounded wire. The 3 wire GFCI cannot service 120 VAC devices on the circuit because it would see the current to a neutral as an imbalance. Also there is not a neutral in a 3 wire 240 VAC circuit.
The 4 wire device monitors the current on the two hot wires and on the neutral. It is called a 4 wire 120/240 VAC device because the circuit uses two hot wires, a neutral and a grounded wire. The 4 wire GFCI can service 120 VAC devices because there is a neutral and the GFCI is monitoring it.
It appears the EZSwitch30 requires a 4 wire 240 VAC circuit because the specifications say “NEUTRAL REQUIRED”.
Hot tubs and 240 VAC are potentially dangerous and I don’t want to speculate on ddlux’s situation. The National Electrical Code places a lot of requirements on hot tubs and the authority having jurisdiction has the final say.
I am just guessing here. Maybe ddlux’s GFCI is a 3 wire one and that’s why the EZSwitch30 is causing it to trip. Perhaps the 3 wire GFCI could be swapped out for a 4 wire GFCI. I am not an electrician and so don’t take this as any authoritative info. (heavy disclaimer)