How often have you been cleaning your tile floor? As to a safe way to clean the tiles I'm not an expert as I've had similar marble tiles in 2 showers for years but never had a problem.

Info on maintenance of shower tiles:

A shower floor should be cleaned at least weekly, but ideally after each use to prevent soap scum and mildew buildup. A quick wipe down with a squeegee or absorbent cloth after each shower can significantly reduce the need for more intensive cleaning. Frequency:

• Weekly: A thorough cleaning of the shower floor, including grout, should be done at least once a week.
• After each use: Wiping down the shower floor with a squeegee or absorbent cloth after each shower helps prevent soap scum and mildew.

Factors influencing frequency:

• Foot traffic: Areas with more foot traffic, like the main bathroom, may need more frequent cleaning.
• Individual habits: Some people prefer to clean more often than others.
• Severity of buildup: If soap scum or mildew is accumulating quickly, more frequent cleaning is necessary.

Tips for maintaining cleanliness:

• Squeegee or dry: Use a squeegee or absorbent cloth to dry the shower floor after each use.
• Ventilate: Ensure proper ventilation in the bathroom to reduce moisture and humidity.
• Use appropriate cleaners: Choose cleaning products specifically designed for shower tile and grout.
• Seal grout: Seal grout once or twice a year to help prevent staining and mildew

It appears that you have a very common issue that occurs when you use a marble mosaic tile for your shower pan. What you are seeing is not staining that you can clean - it is actually the tile retaining water. Do a Google search for issues re: "marble mosaic tile in shower pan turning dark in some places" or something like that. You will fine TONS of posts on various forums regarding this issues. You can add "Houzz" to the end of your search in order to pull up all of the related posts on here (the search bar in the site does not work well in my opinion).

You have some issue related to water in the shower pan. Do you know how the shower pan was constructed? That will help narrow down the reasons for the water retention in the marble tiles.

Also, were the tiles sealed? There are differing opinions re: whether marble should be sealed in a shower. The issue is that an impregnating sealer will allow water vapor to pass through the sealer into the tile - however, once the vapor returns to a liquid state = water, it becomes trapped inside the marble (especially if a surface waterproofing material was used on the shower pan vs. the traditional "water in - water out" shower pan.I

Thank you!

It wasnt done correctly. Only a full rip and redo of it all will fix it.

I does look like water isn't draining fully under the tiles and I would worry that you are looking at mold that is growing under there. I don't think anything you can do topically will fix that and you probably need to rebuild your shower. Unfortunately, it's an odd shape so you can't just remove the tile and drop in a solid surface shower pan. (which might also be impossible to waterproof, as the water could leak down the walls to under the pan. I fear you are going to have to rebuild the shower. Educate yourself on waterproofing and make sure your contractor is doing it correctly. Maybe choose porcelain tile.

" I don't think anything you can do topically will fix that and you probably need to rebuild your shower "

My exact thoughts from the picture.