The mentioned trinket is Tome of Unstable Power.
The equip effect reads “Your harmful spells have a chance to create 1 to 3 arcane illusions…”.
The text does say that it only procs off of harmful spells. Mistweaver monks, and monks in general, do damage mostly via punching and kicking. I sat at the dummy dpsing for a good while and the only ability that I cast that seem to proc the trinket is Chi Burst, and it takes me ~11 Chi Burst cast to even proc the illusion. The rest of the kit does not look like it would proc, but maybe Jade Lightning and Chi Wave would considering they are harmful spells. Regardless, why even bother with giving Mistweaver this trinket as possible loot drop where they cannot utilise its proc effectively?
Meanwhile my DH guildie is telling me that the trinket is stupid OP on them, because they apparently “cast” a lot of spells, the dmg offset would even be attractive enough for them to wear an intellect trinket. Please look into this.