Magician Casting Speeds

Using those same weapons (Nocturnal Staff = 6, Umbrella = 5, Sword = 4) I could see absolutely no difference in Fire Arrow casting speed.

Nocturnal Staff - 50/60 s per cast
Yellow Umbrella - 50/60 s per cast
Sword - 50/60 s per cast (all without booster)

I checked all of them over 10 casts and they came out to exactly 500/60 seconds in every case.

edit: That's 72 per minute and you have 76, I will test some other skills you have marked at 76 but I think Fire Arrow is slower than other magic attacks.