How to fix bathroom tiles falling off

You don't "pad out" a wall and then tile it. They had a couple of inches to work with. So stud the wall with 2x2 or 2x4's flat and cover with cement board, waterproof, then tile. It probably would have been faster than what they did.

You're going to have to remove all of that wall and redo it.

Regarding the gap, baths almost never fit the space exactly. Apart from the obvious problem of building and preparing walls millimetre-accurately, if the bath fits the space too closely then you're going to have extreme difficulty actually getting it in there. Pythagoras says that dropping the bath in anything less than perfectly parallel will make the bath take up more length than there is space for, so it'll jam partway down. The result on an acrylic bath will likely be damage to the bath rim.

it is entirely normal to fix a batten along the end wall to fit the gap (normally at the non-tap end), and cut tiles to fit over that. The tiles here could be round-edged (trim) tiles, or they could be normal tiles with a trim strip to finish them. The tiles should have a slight slope towards the bath so that splashes will drain back, but they should be flat enough that this is a good place to put soap, shampoos and so on. If the gap is small enough then just a trim strip may be sufficient.

Or as JACK says, finish the wall accurately with an appropriate type of drywall, and tile on that. If you want to pack the wall out, that's the right way to do it.

When you agreed to it as a solution, it was sensible. Don't blame yourself on this one. The problem isn't you agreeing to it, the problem is simply the half-assed way they've gone about it.

I disagree with some of the reasoning of the other answers.

1. They should have furred out the wall. Everyone here agrees on this. They could have framed out more or just added shims/drywall layer... lots of methods here depending on how far you go out.
2. Point that no one has brought up. Most bathrooms - normal ones - not the fit-for-a-king master... they are basically built around the tub or shower pan. Yours fits that bill. Why the hell would they even frame the bathroom without the specifications or the tub onsite. That is f'ing crazy and amateur amateur. Who was the general contractor and were they overseeing anything?? I would be worried about the entire house honestly.
3. That is not a flat/proper substrate to attach things to. You can't just put tile on anything!!!
4. I am not sure what the material is but it isn't thinset and if it is mastic it is a really cheap type. "Stuff" that you use to install tiles sticks to the tile. It doesn't bind to itself more and form cow patties. The binding material is "who-knows" but way way off. No matter what this stuff was going to fall down. That is given the first three points were done right.
5. These are large large tiles. To install them properly (with thinset or similar material) you would back butter each piece and apply/trowel the thinset to the wall. The installer plopped a few big drops on each tile and stuck it on the wall. Even if steps 1-4 were done right the tiles would fall off.

So yea you have to take down the whole bathtub area. Even given that things 1-3 may not apply to the rest of the area, #4 and #5 will and these tiles will fall off too. The good thing is there is a high chance you can reuse these tiles if the rest were done the same way.

TL;DR

Five-spotting is a really bad practice.

Per https://www.daltile.com/how-to/how-to-install-tile/how-to-install-large-format-tile:

When installing large format tile, there must be at least 90% mortar contact

---

It is hard to say whether the compound they used was mortar so I am not going to gripe about that.

The fact that they should have furred out the wall has already been covered in other answers.

What I want to concentrate on is making you aware of the technique which they employed to put the tiles up and it's called five-spotting. An utterly heinous method used by sub-par contractors. Even if the correct compound and furring was used you would still have been prone to this tile issue because they severely cut corners with your install.

Assuming that the walls and floors were done by the same contractor then all of the tile work NEEDS to be ripped out because I am 99.99567% positive that five-spotting was used for everything. Right now you are pitted against a neverending slew of tiles falling off the wall and possibly hurting someone, and your floor should start showing defects as well if it already hasn't.