Xbox One Controller: Left stick axis snaps to cardinal directions?

I am building a game with grid-based movement similar to Final Fantasy Tactics. Left stick inputs are interpreted based on the camera's rotation, so if for instance the camera is at 180 degrees, left moves the cursor one square to what would be the right at 0 degrees. This works as intended at 90 degree angles, but at 45-degree tilts (45, 135, 225, 315), I run into this problem.

It seems as though the Xbox One controller has a range around up, down, left, and right where it simply snaps to those cardinal directions. In other words, I try to press down-left, but if it's close enough to down, it gives Unity an x-axis value of 0, causing the game to read that as a "down" input. Has anyone encountered this problem before? Is there a fairly easy way to fix it?