The tsunamis mentioned in replies are localized in effect. Glacier drops/breaking dams are catastrophic regionally, but not to the extent of creating a tsunami that travels thousands of miles to inundate tropical islands, which are the subject of the original post.
Those islands sprout along the pacific rim and are susceptible to tsunamis from earthquakes. Glacier issues would never have troubled them.
The glacial melt caused the sealevel to rise, which had an impact on all landmasses.