Remember "heated air rises". The wiggly red lines represent heat waves rising upward.
Diagram 1:
Haven Spa with the insulated cover on the spa.

Heat from the pumps is the primary source of heat for the water. The heater is a backup source of heat.
Heat from the pumps warm the air chambers located underneath and on the sides of the spa.
Heat from the pumps warm the spa water. The insulated cover keeps the heat from rising up and out of the spa.
Excess heat buildup is removed by the DAIT system.
This design results in real energy savings for the spa owner.
Diagram 2:
Haven Spa with the insulated cover removed.

When the insulated cover is removed, heat rapidly rises from the water into the atmosphere.
The pump motors continue to create heat, which continues to warm the spa water.
When the therapy pump or pumps are turned on a great deal of heat is generated.
None of that heat is wasted. It continues to warm the spa water.
In a Haven Spa, the water temp may actually rise, without the heater coming on, after the removal of the cover if the therapy pumps are run.
This is the best design for a modern hot tub ever. The expensive to run electric heater is used only as needed.
This is the thermodynamics of a "thermal pane of thermally sealed" spa design.