the cooldown is only 45sec so it's very short. it's up when you need it.

and yes, if you use the pyrorockets you "on use" trinkets gets a 10sec cooldown, and if you use you trinket first your pyrorockets gets a 20sec cd.
(only offensive trinkets)

Other than that, I'm concerned about losing a lot of stats with engineering, and I'm not quite convinced (prove me otherwise!) that pyro rockets are the difference between a kill and an enemy at 10% hp that gets an instant heal.
to kill or not to kill, that is the question
dead is dead and alive is alive, pyrorockets can chance the status of your enemys from alive to dead without a gcd