Wiring a 220v pump with 2 hots to a controller
Ok, hold on.  Are you sure you followed the instructions? Is your model number the same one in the instructions?   Reason I ask is, having to bring out neutral just for this is stupid.  That transformer inside the relay ought to be 240V.    

So I think you got a defective one, or at least the wrong one.  

Normally thermostat circuits are 24V, though this transformer may be doing something a bit different - I'd consult the factory.  

The more standard way to do this is a 40VA 24V junction box mounted transformer (for about $11) which can mount anywhere, common thermostat cabling, and then a common air conditioning relay (about $13) inside a large junction box ($9).  This has several advantages: it will switch both poles, so when the equipment is off, it's really de-energized.  It operates on standard thermostat voltage, so you can use more readily available standard controls.  And if you have a furnace with surplus 24V power, you can just poach power off that instead of using your own transformer.  Also it's made to switch inductive loads, which is not necessarily true for relays like this.