BOM do know a lot about these types of events and in the past earthquakes of magnitude 8.0 at the Solomon Islands have caused tsunamis of about 10cm on the North Qld coastline.

Tsunamis of 10cm do not cause major damage and a land based warning is inappropriate

But, as I wrote earlier if there is a tsunami wave they will detect it and issue whatever warnings are required.

They may have to issue a marine warning/advisory later, will be interesting to see what happens

There are 10 buoys in event mode in the Pacific Ocean at the moment. If you click on the pulsating diamonds (buoys), you'll see some very interesting movements have occurred.

Interesting articles on the web...

"Earthquake acoustics offer hint that a tsunami is imminent, researchers find" - phys.org

"Chile set on GPS-based tsunami warning system" - newsxs.com (SciDev.com)