How to better waterproof the shower area?
Yes, the tile joints do let water pass. The grout is porous, and additionally does not seal tight with the tiles as it ages (causing it to actually pull some water in via capillary action). Many tile materials are not waterproof either. 

Bathroom tiling is only "waterproof" in the sense that it is a finish material that will not be damaged by water. It does not serve to create a waterproof enclosure; that needs to be built behind the tile. If that was not done correctly, any attempts to seal the grout and tile will at best only serve to delay the inevitable.