The air from each seat blower splits out to two TED modules, one for the seat bottom and one for the seat back.
At each TED module, the airflow splits into two again. Half the air flows over the top of the TED and half flows over the bottom. The air from the top half of each TED is ducted into the seat cushion. The air from the bottom half of each module is exhausted under the seat.
The TED module transfers heat from one of its sides to the other side. If set to heat, the top half will get hot and the bottom half will get cold. Hot air goes through the cushions, and cold air comes out under the seat. The TEDs are mini heat pumps. For cooling, they work the other way around.
There's no way for this setup to work without the fan going.
BTW, please name any car that has cooled seats that doesn't have a seat fan.