So. It makes perfect sense really. Think about an ice cold water bottle on a hot day. Picture it. Is the exterior of the bottle wet, or dry? Wet. Because when hot, damp air touches a cold, dry object, it condenses into water droplets on the object. Now imagine the bottle is your egg, and the hot summer day is the inside of the egg cooker. The steam from the boiling water in the bottom of the cooker condenses and forms water droplets on the egg. Once the droplets get big enough, gravity takes hold, pulling them down. Down, back into the bottom of the cooker, to be boiled and start the cycle again

When you have a lot of eggs filling the chamber, you have a lot of surface area for water to condense onto, which means a lot of water droplets making their way back down to the bottom. Conversely, when you have one egg, there is less cold area for water to condense onto, so most of the steam goes out of the top of the cooker, which means less droplets make it back into the water. Therefore, you need more water, since a larger percent of that water is escaping, to produce the same firmness of egg and the same cooking time as multiple eggs.

The way the timer works is a bit more technical and I haven't taken one apart yet to find out which of the two mechanisms I'm thinking of is used, so can't tell you for sure HOW it works, but I can tell you WHY it works. Water boils when heat is transferred to it, we know that much. There's a heating element under the metal bowl at the bottom of the cooker, which transfers heat through the bowl, into the water. But we can also think about it as the water cooling down the bowl, and thus the heating element, because that is also happening at the same time. As long as the water is cooler than the heating element, which it is all the way up until it turns to steam and is no longer touching the bowl, it is stealing heat from the element and keeping it at a steady temperature. Once all the water boils off, the heating element can no longer stay cool, and rapidly heats up. That's when the cooker decides to turn off and voila! Perfectly cooked eggs.

The great thing about how they work is that the whole process is very easily reproducible, allowing for perfect eggs every time as long as you put the proper amount of water into it.

Hope that helps!