Thank you for the update Melixy.

I do have a few more questions regarding your PC and controller.

1) What operating system do you have?
2) You mentioned this happens with the PS4 controller, but does the same thing happen with the 360 and Xbox One controller you listed in the first post?
3) Are you using the same USB cord for all of the controllers? Do you have another you can test?
4) Do similar issues appear in other games?

You can try deleting the whole FFXIV folder in the My Documents folder (not just the UI settings) and see if that has any affect. Just be aware that this will delete all of your user settings (hotbars, gear sets, etc.)

You can also try a clean boot. Simply open the task manager and select the 'Start up' Tab. Disable everything here and restart the PC. This will make sure that no background processes are interfering with the game.

We hope we can be of assistance in helping you enjoy the exciting world of Final Fantasy XIV!