Currently the SeaStorm notification system works a little differently than you might expect, so here is an explanation of how the process works internally.
When you first launch SeaStorm, it gets a list of active storms in the region(s) you have activated. After 3 hours (or whatever you have notification frequency set to) it will check the active storms again, and compare them to the last time it was checked. If a new storm has formed, or a previous storm has been upgraded in "type" only (depression -> tropical storm, or tropical storm -> hurricane) you will receive an alert. It does not issue alerts for updated advisories or hurricane categories (yet - both will be included in a future update).
Also note that each time you launch SeaStorm (or refresh SeaStorm's home screen), the list of active storms used by the notification system for comparisons is updated, and the notification countdown clock is restarted. So if you open SeaStorm and a new storm is listed, you won't receive a notification about that storm, because you already saw it. :) The countdown clock is also restarted when your device first boots up (unless you're running on the SD card, in which case it won't start until the first time you've manually launched SeaStorm after a reboot)
I hope this clears up any confusion. Feel free to e-mail me if you have further questions.