Interesting that you mention timing, the trick is to listen for the "thump" as the mortar fires then wait a bit and press the shutter release.
If you're lucky the shutter opens just before the charge bursts so you catch the full "flowering".
This is one case where a digital camera comes into its own because you can shoot a bunch, pick out the ones you want and anything you don't doesn't cost anything.
Also you can see immediately if you're getting it right so you can adjust exposure time and aperture as needed.
In the few minutes the fireworks display was happening I took 76 exposures and I promise you there was a lot of garbage!