Shower – just seal a leak in the shower

From your last picture, the water proof membrane goes between the tile and concrete in the shower. It should be overlapped and sealed all the way to the drain so that any water that gets around any cracks or through the porous tile/grout can only escape through the drain. Once it reaches the concrete, it's too late. Like sharptooth says, this is something your neighbor needs to solve.

Edit: Here are a few sample waterproofing products that would be installed under the tile:

Aquashield

Shower Pan Liner

Note that it may be possible to add some silicone caulk around any gaps and apply some sealer on top of the tile and grout, but that solution would be prone to failure over time.

You are absolutely right that the floor will move independently of the walls. The movement when an adult steps in is not as much as a full bath of water, say, but it is still enough that you need a flexible seal of some kind to avoid water pooling and mould growing.

I asked a similar question which @ChrisF answered very well which suggested that caulk should be flexible enough to cope. That is what I did, and so far I have had no leaks (I have taken the panels off to check every now and then)