For some reason, I can't find any weak auras out there which announce when one of the opponents in an arena uses a trinket in chat, so I've made one myself.
You make an announcement in chat whenever an opponent uses their trinket, and the cooldown appears on the left.
This doesn't work with the human racial yet, I'll have to add this.
You can change where it announces it if you go to the Actions tab, its the Message Type dropdown bit