In short, yes it does. The thing to note is that Composure is NOT a focus effect. It is a mana/hp regen effect (+3 to each). Also, all the more 'cryptic' effect names that add hp/mana regen and/or ATK have been removed and the actual details of the effect have been tagged to the item. (That screenshot is a bit dated)
The FOCUS effect on this item is Speeding Thought and that does NOT stack with other forms of spell haste. I.e., it will not stack with Spell Haste 4, Quickening of Solusek, etc.
The item lore says this thing is a vibrating metal earring. ..wouldn't you think that'd get extremely annoying, having a vibrating earring on all the time?
We got one of these yesterday just off a random trash mob, I think it was a kyv. It's the first time I've seen one and we've cleared a lot of mobs heading to raids so it seems to be fairly rare.