I am assuming the original thermostat had only two wires connected just like any electrical
switch would. When thermostat knob is turned to the off position does refrigerator
stop? If not the both of the two wires on thermostat may be connected to the same split brass terminal.
There are three basic mechanical thermostat temperature ranges Freezer
and and drink cooler thermostat. Small refrigerator thermostat temperature sensing small tube is connected to evaporator. Are you sure this temperature sensing tube is correctly located.