Shot in the dark, but FFXI polls directinput for both a queue of recent actions *and* a current controller state. I haven't traced which is used for each action, but I'd bet:
Your controller stick *actions* are bogging down the queue (ffxi only polls 16 per frame and dualsense can send more than that)
FFXI is reading the state for joystick direction for motion
FFXI is reading the queue for button presses, so it has to catch up to actuate them
Potential solutions would be to use DS4Windows or something else to map to xinput or raise/uncap framerate
may also be fixed on Ashita4(my controller hook pulls 64 per frame, discards stick input in dead zone, and gives ffxi 16 so it doesn't bog down as quickly)