I attribute the phenomenon, to the loss of half the fish structure when filleting the second side. I have adapted my process to compensate for this as needed. (A) being right handed one side is always more ergonomic for me. This happens to be the left hand side of the fish. (B) Starting on the left side of the carcass, I make a cut behind the head. Followed by a cut along the spine, only as deep as the rib bones. Once I clear the rib cage, I plunge the knife deeper into the carcass and out just behind the vent. Slicing along the spine until I reach the tail. (C) I do NOT cut thru at the tail, instead, leaving the partially cut fillet, still attached to the carcass, (ribs, along the belly and at the tail).
(D) I then flip the fish over and repeat these steps on the second fillet, except this time I cut thru at the tail and the belly area, fully freeing the fillet from the carcass. (E) Flipping back to the first side, I complete the process and free that side from the carcass.
It is my experience that leaving the first fillet, intact and partially attached, helps me control my cuts on the second side. Works for me. I'm not real fast but I'm pretty thorough and don't leave much meat behind.