What you are talking about is not made clear by the picture

It's not normal for the edges to have more grout. All the joints should be consistent. Even without expanding the photo I can see the edges of the sheets. And yes, the bullnose edges should line up with the remainder of the tile grout joints in the field.

To do glass tile, one must be patient and carefully lay out the tile prior to setting to ensure all the joints will line up when set. It takes A LOT of time.

Most times the surface has to be "adjusted" with mortars and build up areas to allow for all the joints to line up.

Check this guy's site. Jimmy Reed Rock Solid Tile in CA. He's probably the best in the business. His glass tile work is stunning. http://rocksolidtile.com/

Look at his glass work on pools and spas and you will see the correct job results. He has several videos on You Tube if are interested in his process of setting.

here's a more close-up photo.

Your contractor giving you BS. Sheets should not be visible.

What's the narrowest grout size that can be done? Is it possible that the grout size between mosaics within a sheet is too small such that the grout must be wider between sheets? (heard this from someone; not sure if true or BS).

That is BS.

The grout spacing on the sheets is what should be consistent throughout the rest of the tile.

If it's wider, the result will be what you have now. Yes, BS.

I think the grout lines between sheets should be the same as grout lines in between the sheet. I have similar glass tile in my spa and enclosed a photo. I do not see the individual sheets. Perhaps when the water falls over the tile it will look less conspicuous. I would be hesitant to have it redone since it was not done right the first time and a redo will have even more challenges and may not look better but may look worse.

No tile expert here, but I believe a redo would require demo and destruction of the tile, prep of the surface, purchase new tile and get someone else who is careful to install it.

I am sorry this happened to you, Allen, I hope you get it resolved.

Sonja, that's a beautiful spa. Would you mind sharing what material was used on your spa/pool deck? It looks like porcelain tiles.

Thank you, so glad you like it. I do not mind sharing. The spa is glass tile; inside the spa is Primera stone, same as inside the pool, the pool coping is Leuders limestone, and the deck is Travertine pavers.

Thank you, Sonja :))

They could have done a better job, but I think that is within the typical range of installations. I'm very picky but would have a hard time asking them to rip out the tile and do it over - as others have said, it would probably end up looking worse than before.