A shorter casting animation does not always mean a shorter cooldown.
For non-static skills, this Interlude implementation multiplies the configured reuse by the relevant reuse-rate modifier and by 333 / attack speed: Casting Spd. for magic, Atk. Spd. for physical skills and songs/dances. Faster casting and shorter reuse are related here, but still separate values.
Static skills start from their configured fixed reuse instead of that speed/rate branch. A separate class-balance multiplier still follows. A successful Skill Mastery check can set reuse to 0.1 seconds and display the ready-again message; this does not establish a universal proc chance.