I think that you are referring to a newer design, called an “Over-Balanced First Stage.Second stage does not influence IP but an unbalanced second IS influenced by IP. When you set the cracking pressure on an unbalanced second you need to do so at a tank pressure where it will see the highest IP (high tank pressure for a piston and low pressure for a diaphragm). If you set your unbalanced second at high pressure, then when the tank pressure drops to 300-500 psi and IP rises on a diaphragm first (even on a balanced first it can go up as much as 10-12 psi) it may cause the second to free-flow (if your second was tuned at the edge of easy breathing). Hope that explains it.
Over-Balanced Regulator001 by John Ratliff, on Flickr
Because my understanding of a balanced first stage is that it really does not respond to fluctuations in tank pressure. But the “Over-Balanced First Stage,” by Aqualung, actually built in an increase of the IP as the diver descends, according at least to this advertisement.
The original balanced first stage was the Calypso, by U.S. Divers Company, and it did not have a fluctuation of the IP with changing tank pressures.
IMG_1824 by John Ratliff, on Flickr
SeaRat