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
The answer you are looking for is... it is up to you.
Baseboards are there...
To make sure a wall does not get kicked or damaged at the bottom.
To hide flooring gaps.
For decoration
For a good excuse to buy a mitre saw.
Depending on the type of flooring you install you will want to adjust your base boards or even install different types.
Michael says you may need a base shoe - warning I am an anti-shoeite. Why why? Why the extra piece at the bottom that gets broken or comes loose. I have never been in a super upscale house and saw a shoe stuck to the bottom of trim.
So some guidelines:
Carpet = 1/2"... if you are getting some super dense stuff maybe a little more. If you are getting stuff that might not even be considered carpet (I call it astro-carpet) then maybe less. It should be tucked into baseboards. Meaning if baseboards install after you should slightly smash down carpet at edges.
Wood = You should be installing after and lay it on the wood. So not all floors are exactly level-perpendicular should you have have gaps underneath some sections. This is OK and aesthetically each wall should be laid out to look good and join at corners well. Note that if you are leaving 1/4-3/8" you have the option of getting trim that is thicker to cover this. You can also find trim that is thicker at the bottom, which is all you need.
Tile = You also should install it after as you should not be grouting between tile and baseboards. If you were a pro and had installed a certain tile before I guess you could leave the baseboards and slide tiles under... that is not normal though. For gap on tile I like 1/8" all the way around. Two reasons... It shows better. If one tile is slightly slightly higher you won't notice as much if baseboard was sitting on it. Also you won't notice grout issues or divots that are perpendicular to baseboards as much.
Vinyl/planking/engineered - treat these like wood.
I have done shoe moulding on two out of my last maybe 50 flooring remodels. One was because my guys had uneven and big expansion gaps (install mistake). The other the lady explicitly wanted it even when I tried to talk her out of it.
How big the gap is... well it really comes down to what looks nice? I would for instance welcome a larger than I want gap to forgo shoe moulding (I know those two are not really related).