As you said, it looks like a stud wall with PB and then plaster skim on it.... Not a good choice for a shower.
The tile adhesive has also not been applied correctly for a shower (it should have been a thin skim (3mm thick) of waterproof adhesive with ridges on top rather than just the ridges on the back board.
Quick fix: file the hole with some more plasterboard or a bit of ply. Don't bother to re-skim, just level up with a good waterproof adhesive and fix the tiles on again. You won't be able to get the right thickness of adhesive on the right hand tile - so that one will be no better off than before.
Longer term, this does need fixing since there is a fair chance that water is getting through in other places. Hence there is a risk of it feeding dry rot etc.
To fix for good:
You will need to replace the backboard with something that is not absorbent, so either WBP ply with render over, or use one of the cement type ready made boards like Aquapanel that are designed for wet service areas.
It is handy if you can arrange that the wall surface runs down *on* to the tray (i.e. not beside it). Seal round the tray with good silicone. Now retile using a full bed of adhesive and then grout with waterproof grout. Treat with something like Lithofin grout protector to keep it looking nice and add yet more water resistance. Finally silicone all the joins (I prefer to silicone the vertical corner joint between the tiles rather than grout it - that way it is better able to resist any movement that may occur).
Here is one I did earlier:
Don't know.