I have no practical experience with contactors but read that chatter can be caused by low voltage. So perhaps the supply cable is too small a CSA or too long? or loose connection? eg When immersion heater turns on the voltage drops causing the contactor to drop out, immersion heater switches off, voltage rises, contactor turns on again. Repeat rapidly.

or perhaps the immersion has a high inrush current which causes the same effect (eg dipping the supply voltage). Perhaps a contactor with a longer drop out time would work? Perhaps a time delay relay in there to get past the in rush?

Incorrect or faulty hold on circuit - contactor closes, hold on contact opens, contactor opens, hold on contact closes, contactor closes until the coil burns out.

If it's the thermostat wired into the control cct it could be the stat which is intermittently making & breaking.....