Ohh ohh, it sounds like he has got his setting out wrong.
I'm going to give you and everyone else a list of questions to ask before any tiling is started. You can use this a check list.
Firstly let's go with the basics
If your having mosaics, the most important thing to bear in mind the surface that the tiles are going on must be flat and even. If you can picture glueing tissue paper on the surface any deviation will show. That's what your dealing with when having mosaics. You have any small bumps etc in the surface the mosaics will ripple and look terrible.
Cheap tiles... don't do it! They are cheap for a reason, normally they are bowed like a banana, and the sizes of them can vary from box to box. Always when purchasing tiles check they all have the same batch number.
Secondly this is one of the most important things and OP this one is for you. The setting out of the tiles. A good tiler will run a tape measure across the area and then divide the area by the size of the tile and the grout joint. So in your case OP he should and would have known that there would have been a gap. He has already done the tiling which is showing up like a baboons bottom, it's just plain wrong. He has three options now, the first is to rip them if and start again and increase the size of the grout joint slightly so that the shortfall is no more. The other option is that he puts a cut tile on either side, so it is then flush with the work surface edge. Thirdly but it could look messy is to install a trim, not a cheap nasty plastic trim but a flat bar stainless steel one or similar.
Always tell the tiler in advance of the works you want as fewer cut tiles as possible. This applies to walls and floors. He should discuss with you the setting out before commencing the works.
Surface priming, if the tiler starts using pva to prime the walls stop him!! It is the worst possible thing to use as a primer as over time if it gets moist it disintegrates resulting in the worst case scenario the tiles becoming loose. He should prime the surface with a primer fit for purpose and pva is not!
Pre mixed tile adhesive is a no no, it contains to much water and over time when the adhesive drys it looses its adhesion.
The most serious red light warning sign is when a tiler 'dots and dabs' basically some idiots will try to install the tiles by applying dots of adhesive to the back of the tile. This leaves voids behind the tiles which can result in tiles dropping of walls and tiles cracking on the floor. The adhesive should cover at least 85% of the back of the tile, when this is installed it is then positioned and moved slightly to give full coverage.
Grout, this can make or break the installation. The client (that is you) should always be the one to select the grout colour. If they suggest plain white in a kitchen remember it won't always be white.
Please remember this, if your not happy then do not hand any money over. You have to be honest and tell them your concerns and you want this sorted.
I hope this helps a little.