The two pieces
NOAA’s National Data Buoy Center describes a DART system as an anchored seafloor bottom pressure recorder and a companion moored surface buoy for real-time communications. An acoustic link sends data from the recorder on the seafloor to the buoy. The pressure record is a measurement of the water column. It is how the open ocean reports a tsunami that is already passing the instrument. It is not an earthquake prediction and not a forecast of where the next earthquake will be.
Standard reports and event reports
The same description says the system has two reporting modes, standard and event. In ordinary times it sends scheduled reports. When its detection software identifies an event, it switches to event mode and sends data more often. DART II became operational in 2005. A capability NOAA states for DART II is two-way communication between the bottom recorder and the tsunami warning centers and the buoy center, using the Iridium satellite system, so a center can request event mode or pull higher-resolution data.
What you are seeing on this website
The live map can show a local snapshot of DART stations from data/dart_stations.json, the same way the About page describes it. A marker that pulses after a large Pacific earthquake is observational context. It is not a warning, not a wave height, and not a substitute for tsunami.gov. The words warning, advisory, watch, and information statement are defined on the tsunami alerts page. What a person on the coast should do is the tsunami preparedness page.