The article is very thin on details. For example, why not use a mechanical timer like many other appliances did and still do? That's the kind of detail an IEEE reader might appreciate.
A timer doesn't work because it takes longer to boil three cups of water compared to one. The bimetallic mechanism is agnostic of the amount of rice being cooked.
In the design being described there is an outer water reservoir where the water is being boiled away specifically as a timer. An alternative would be to have a bimetallic strip detect when the rice pot comes to temperature, lower the temp, and start a mechanical timer that could be set by the user. The advantage would be a significant energy savings vs. boiling water away as a kind of crude timer.
The 20 minutes is for ideal conditions. The article explained the goal was to boil away the water and then reduce the heat. The time needed may change with different ambient temperature or humidity.