Sounds to me like one of three things:

A) Faulty hardware. I'm not exactly sure what you mean by "FFXIV controller," was there some specifically branded USB gamepad for FFXIV or is it just some generic USB gamepad? I'd double check that the drivers for the device are properly installed.

B) A software conflict. Some other software could be continually sending the same keypress signal as whatever the analog sticks send. Do you have any sort of "homebrew" controller software installed to either custom map keybinds or something like Motioninjoy to use a standard PS3 controller as a PC controller? That stuff typically is the culprit with these kinds of issues, I know when I tried motioninjoy myself it gave me a world of issues and side effects even after uninstalling.

C) Is there some sort of calibration settings in the gamepad driver/software? If its reading the stick being centered as the stick being physically held down in a certain direction, when the stick is where it physically rests it'll constantly be sending an "up" signal even though you're not touching the controller. You might need to reset the calibration to let it know where the stick sits naturally.