This happens with both my Steam Controller (my preferred controller. Don't judge me.) and a usb wired 360 controller. I prefer to play FFXIV w/ controller as I learned the game on PS3 and that's how I feel comfortable playing the game.
PC Specs:
i7-8700k
EVGA GTX 1080 FTW2
32GB RAM DDR4 (3000)
ASUS ROG Maximus X Hero (Wi-Fi AC)
Windows 10 64-bit
I'll be moving in a direction then I let go of the analog stick or try to change directions and my character will still be moving for a second or two in the same direction.
Or I'll try to press the triggers and either it won't register I've pressed them for a sec or two OR when I let go to use a different skill in a different cross bar it thinks I'm still pressing the trigger for a second or two.
It's intermittent, but it happens frequently enough that it's getting me killed in combat (as my character will just walk into AOEs), disrupting my combos, and makes the jumping puzzles downright impossible.
It doesn't happen in any other game, so I think I can say with certainty it's not my computer. Any and all help would be appreciated.