Earthquakes damage bathroom tiles?

Yep, this can happen if the tiles were not installed properly or the mortar is old enough to break down. Grout should be used between tiles only where it is not butting up against another wall of tile or against a fixture (such as a tub, sink, or countertop). Where tile meets a fixture, a silicone or siliconized caulking should be used to ensure a seal for moisture as well as flexibility for movement in the house (all houses do settle over time so this is imperative to follow). Non-sanded grout should be used in gaps less than a quarter of an inch and sanded grout should be used in larger gaps between the tiles or on any floor tiles that have been installed.

Check the consistency of the mortar behind the tiles that have come free and check for excess moisture and a “rotten” feel to the old mortar. If the mortar crumbles easily or feels rotten then you are most likely looking at a completely demoing the old tile and reinstalling it. You can do a temporary fix with premixed tile grout/adhesive to use to glue the tile back into place, but it is only temporary.