Hot Tub heating issue?

From what you are describing it sounds as if the power lead is going straight through the overtemp sensor to the element and not through the thermostat as it should. This scenario would let everything run up to the point of the thermostat turning off then the element would keep running untill the overtemp shut it down. Make sure that the hot wire goes through the thermostat and then through the overtemp so you get control from the thermostat.