You have to have a neutral wire going to the fan, otherwise it wouldn’t work. The reason they state that neutral is required is that sometimes you won’t have access to the neutral wire where you are trying to wire up the controller. For example, the switch to the light in my bedroom has two wires, both black. This is because the line (or hot) going to the outlet is being broken by the switch to turn it off and of. The neutral wire for this outlet is somewhere else. Therefore, I could not wire this device into my switchbox in my bedroom because there is no neutral wire ACCESS. But everything that is wired has to have a neutral wire. That’s what completes the circuit for the electricity to flow there.
So, assuming you want to wire this in to control the light and the fan with the two sides of this relay, your fan should have 3 wires coming from it. A white, a blue and a black and your wires coming to the fan should be black and white. I am willing to bet that currently it is wired up as wall black wired to fan blue and fan black and the two whites tied together. Right? if so, then what you want to do is connect the relay as follows AFTER TURNING OFF THE BREAKER!!!
Wall Black - Relay Hot
Relay’s Load 1- Fan Black
Relay’s Load 2 - Fan Blue
All 3 whites tied together - wall, fan and relay
Unless you plan on running wires down to a wall-switch to control them, you will not need to use the aux 1 and aux 2 lines but you shouldn’t leave them hanging. cap them off with a wire nut.
Now, that is how you would wire it. I have NO idea if this relay is rated for fans. Not all relays are and some will cause interference and humming. LOUD humming (more common with dimmers though). Also, note, this will not give you speed control. You will have to leave both pull-chains on (and the fan speed to the speed you want). So, whenever the relay is on, the fan will spin at that speed and the light will be on full. Beware, i did something similar for one fan and when the pullchain is left on low speed it takes a while to get up to speed. That’s because fan controllers first spin the fan at high speed for a few seconds to get over inertia and then slow it down to slow. That’s why when you pull the chain it’s at high speed, then medium, then low. RF remotes do the same thing. When you press the low speed button, it first spins at high speed for a few seconds and then slows to low. When you leave the chain on low and use the relay, you go directly to low so the fan takes a little while to get up to full low speed. Also, you will not have manual control to turn the fan or light on when ST isn’t working. So, if ST is down for some reason, you won’t be able to turn on the light or the fan because this is a cloud device type handler.
Speaking of which, you do have the custom DTH for this relay and know how to install it?