In simple terms (or as simple as I can make them):
First, how it works...
In short, water is pressing in on the diaphragm and it will continue to move inward until air stops leaving the exhaust valve and causes the pressure to equalize inside the second stage. How much air leaves the exhaust valve and in turn ow far in the diaphragm moves depends on the differences in depth of the center of the diaphragm and the top of the exhaust valve.
Consider your second stage in a normal swimming position - the purge cover will be facing 20-40 degrees down. Then visualize the differences in the water column. In this position the "average" water pressure acting on the outside of the diaphragm will be equal to the pressure acting right in the center of the diapharagm. (And this will be true in any position.) Now, compare that position to the upper edge of the exhaust valve and consider what it means.
On the average second stage the height of both of these points in the water column are fairly close (i.e. they are at the same depth). Depending on the angle, the exhaust valve may be a bit higher than the center of the dipahragm but it makes little difference as it takes some pressure to open the exhaust valve - in this case we will say it takes about .5" of water, but more on that later.
So in this position, this is what happens: As you finish exhaling, air continues to leave through the exhaust valve until the pressure on the highest point of the exhaust valve is equal to the pressure acting on center of the exhaust valve. Since there is little difference, the diaphragm does not really move in anymore than it woudl on the surface, so no extra pressure is placed on the lever. The result is a "normal" inhalation effort as all of the effort needed to press the lever inward and open the valve comes from the diver creating suction on the diaphragm. For the rest of the example, we will assume the seocnd stage is tuned to have an initial cracking effort of 1.0" of water (very good to excellent by most standards).
Next, consider your second stage facing straight down. The diaphragm is level in the water (all of it at the same depth) and is in fact as deep as it can get relative to the highest edge of the exhaust valve. In this position, the upper edge of the exhaust valve is about 1.0" to 1.2" higher than the center of the diaphragm. This means the water pressure outside the diaphragm is at a higher pressure than the water outside the exhaust valve. If the distance is 1.0" of water, then there is 1.0" of water's worth of pressure.
Since the exhaust valve takes about 0.5" of water pressure to open, there is about 0.5" of water difference in pressure remaining that must be equalized. To do this, air continues to leave through the exhaust valve until the pressure in the case is equalized. By the time this occurs, the diaphragm is pressing inward just like it normally does with the diver creating 0.5" of water worth of suction. This effectively pre-loads the lever and means that rather than having to apply 1.0" of waters worth of suction, the diver only has to apply 0.5" of suction - and from the diver's perspective, the reg breathes easier.
This also sets a lower limit on how easy the reg can breathe. If you set it too much below 1.0" of water, the diaphragm can press in enough to slightly open the valve and cause a slight freeflow.
Finally, consider what happens when you look up. The exhaust valve is now almost level in the water and is at it's maximum depth relative to the center of the diaphragm. The pressure in the case is actually greater inside the case than outside the diaphragm, so the diver has to apply additiona suction to overcome this slight positive pressure as well as the normal amount needed to open the valve. So the reg breathes harder in this position.
Now, where are the lungs in all this? They don't matter in terms of the pressure needed to open the valve. In any position the second stage is in, the lungs have stopped drawing in air when the pressure in them was equal to the pressure in the case of the regulator when it stopped delivering or exhaling gas.
Physiologically, it also does not seem to matter. Consider standing neck deep in a pool. The pressure at the center of your lungs is much greater than the pressure at your mouth, but you don't really notice it and you don't really notice it until you are under water a foot or so (setting the upper limit of the lenght of a snorkel.