First USN tsunami exercise was May 4, 2018 just before Kilauea erupted.
Now a second exercise was just issued.
Except exercises are usually coordinated with other US agencies. Something like this would be coordinated with the USGS (seismic sensor network), NOAA (buoy network), FEMA and other DoD branches USAF (Military Airlift Command) for logistics of relief supplies; USN, Coast Guard for search and rescue operations; Army Corp of Engineers and National Guard to assist local agencies.
Here is a link to all planned tsunami exercises for the past 12 years.
h/t Agent MIB