Hall Thermostat: Common versus Live

I recently replaced my hall thermostat and the wiring connections of the new unit (Moes BHT-002) is below:

I am not an electrician but you can see the connections L, N, Contact, Dry in on the above thermostat and I wired it as follows:

The problem:

If Neutral and Live feeds are plugged directly into the mains and Load is a lamp - everything works fine

If I use the existing wires of my old thermostat (Common, Neutral, Switch); the Thermostat starts acting weirdly and if I set it to 20, every 10-15 seconds it automatically reduces the “set” temperature with 0.5 degrees until it’s so low that the heating is off again. I replaced the thermostat with the same type and the same thing happens. I can only think that Common and Live are significantly different.

Can someone explain what is going on here and how I fix it?