Does this have a hidden cool down? And if so, is it 3x the duration of the buff (in this case, 15*3) ?
They mentioned this item on the Mage Roundtable episode of World of Warcast. According to one of the people in that episode, the "Critical Strike" needed to activate the spell damage boost can come from ANY critical spell that affects the person using it (a Mage's Molten Armor, a Priest's heal crits, etc.); if that's true, then this is one of the best Trinkets you can get as a DPS caster for high-end Instance groups. Felindre
I've read on a number of places (WoWhead, Thottbot etc) that it has an internal hidden cooldown of 45 seconds - essentially 3x the duration as you say.
This trinket can proc from your critical hits - this includes, but is not limited to, things like Healthstones and Potions, along with the usual things(Such as Fireball, Frostbolt, etc). I do not, however, believe this can proc from someone else critting on you(Such as a Priest scoring a critical on you with G.Heal for example). Also, abilities which are unable to score a critical hit, such as Molten Armor(Unless you're referring to the reflected damage) can not proc. this trinket either.
I added some information regarding the expected effective +damage regarding this trinket to the trinket's page. WMA