PulsePoint does not send notifications for all incident types - only for significant types selectable on the Notifications tab (Structure Fire, Traffic Collision, etc.). Incidents of a more routine nature such as medical emergencies, fire alarms, odor investigation, etc. do not have an associated notification (even though they appear in the incident list). The only alertable medical emergency type is "CPR-needed" if selected.
There are also many device settings that affect notification visibility and sound. Within the app use the troubleshooting tool in the header of the Notification tab (... icon) to test your settings.