There may or may not be an easy answer to your question. I would start by calling the grout and tile manufacturers to get their opinion. In general though... You should reasonably expect to get the quality of service you contracted and paid for.
Bottom line is do you think you're getting what you paid for. Not what you think you paid for. If you hire the best electrician in your area to paint your kitchen, don't expect to have the best painted kitchen in town. If you don't hire someone who specializes in tile installations, don't expect to have the best tile work either. If you hire the best tile setter you should expect to have an amazing tile job. You should always check references and try to see examples of their work from the people that you found them through so you have an expectation on the general quality of their work.
Looks like a 3x9" tile (or somewhere around there) which results in a lot of grout lines. On top of that you want thin grout lines. It all adds up to a difficult tile installation. At what point was the contractor aware of the tile you were using? Was it when you spec'd the job or the day he showed up to lay the tile? Usually there's a little bit of blame on both sides.
I'm just a DIY'er but I would have used more tile spacers than he appears to have used (based on the marks in the mortar not the spacers in the photo) and would have scooped out any excess mortar in the joints and off the faces of the tile before everything dried. There may however be other issues that affected the spacing that were outside his control or the budget for the project.
Things may look different (better or worse) once the grout is in. Maybe you want to put grout in a small section before the rest of the tile is laid to get a better idea. If you're not happy talk to your contractor to see what can be done. Depending on the situation it's probably fair that both parties eat some of the cost to redo (or not.) Or just get a different contractor.
What is the standard for variations in grout joints?
When evaluating grout joints, it is important to consider that the
grout is used to adjust for differences in the following:
Variations in the size of the tile Changes in the plane of the
substrate Changes in the thickness of the tile (often this applies to
hand-molded tile) Variations in the rustic profile of the tile The
standards for the manufacture of tile allow for variation from tile to
tile. While the standard details this exactly, it is not uncommon for
some manufacturers to ship tile with about 3/32" difference between
the largest and smallest tiles in a box.
Grout must adjust for these differences between tiles so
understandably there can be some variation in the width of a grout
joint.
Generally, it is advisable to use a grout joint at least two times the
average difference between the largest tiles and the smallest tiles. A
smaller joint will exacerbate the differences between tiles as the
human eye can readily see very small differences as a percentage of
the total grout joint. For example, while a difference of a 1/16" of
an inch may seem small on a 12" tile, this is readily apparent
compared to a 1/8" grout joint.
As the plane of the tile changes, the grout joint allows for this
change. Should tile go over a hump in the floor, the grout joint will
open; when tile follows a depression in the floor, the grout joint
will narrow.
Clearly, grout joints also accommodate both changes in the thickness
and profile of rustic, hand-molded tile.
Perhaps due to these variables, there is not a numerical standard to
which the tile grout joint must conform.
ANSI A108.02, Section 4.3.8 of the ANSI A108 standard says, "Nominal
centerline of all joints should be straight and of even width with due
allowances for hand-molded or rustic tiles."
ANSI A108.02, Section 4.3.10 addresses variations in the plane of the
tilework. This section states, "Finish floor and wall areas level and
plumb with no variations exceeding ΒΌ" in 10 feet from the required
plane."
However, it should be noted, elsewhere in the standards the plane of
the subfloor is required to be similarly flat.
Tile installed by the thinset method is really a surface finish that
will follow the plane of the substrate. As such, variations in the
substrate will be reflected in the tile layer, unless additional
leveling is performed.
Best Answer
Finish laying out the rest of the tiles without the Thinset, using the spacers as you've done so far. You can/should even cut the transition tiles so you get the complete picture. Then jockey them around to see if getting back on the right line makes a difference. You will probably realize it doesn't make much difference but that will be your call. Shifting large tiles can sometimes backfire on you down the road unless you lay them all out first.