the mobs have a chance to drop the items regardless for the most part. Procs just increase the chance of it dropping. For red procs in abyssea for example it increases the chance of getting a K.I. to 100%. (or it may be less ive never not got a K.I. from red proc'd mobs). But everything still has the chance to drop K.I's.

Yellow seems to increase the amount of seals/coins etc dropped (in abyssea) not the amount of a specific type, essentially it adds more "item drop" slots to a mob. But they all have the chance to drop without yellow too.

Blue is like TH on roids, it greatly increase the chance of weapon/armor drops, while a mob may drop without it, it does help greatly when trying to get an item. For example going 1/37 on my Charis Necklace because I couldn't get lucky enough for a dagger blue proc.