Sounds to me like the floor is not flat, which is why you are hearing hollow spots. The tile flex or move slightly due to this and the grout being the weak link cracks. If I am correct the only way to fix this is to remove the tile flatten the floor and have the tile reinstalled.

zargunn:

What is the construction of the floor?

Here in Florida, most homes are on a concrete slab and most tile setters tile right over the control joints in the concrete. Of course, control joints are designed to allow the concrete to move and when it inevitably does, the tile cracks or "tents".

If your tile setter has a grout line over a control joint, consider yourself lucky, but the hollow sound is no good. They must be reset.

"....What do you think needs to be done now? ...."

I think you need to remove some grout and pop out a few of the tiles. I would think you have a bond breaker issue where the substrates' tile prep has failed or the thin-set has failed. Often large tiles are set with the wrong setting materials.

you might discover a pre-mixed thinset like Mastic was used. This would of course be a bad idea and not the right choice for that tile size.

Your builders could have used construction adhesive and cement board as tile prep - that would be wrong as well.

Or maybe the thin-set was right but over watered and installed too thick.

So many things could have been done wrong. Removing a few tiles should point out what the problem was.

Do you know if the installer left room for expansion around the perimeter?

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Thanks so much, everyone! We did not live in the house while the tiles were installed. So I don't have any pictures or don't know any detail of the installation.

Then you best pop out a few tiles and take a look at what is going wrong.

zargunn:

Before you move in, bounce a golf ball on each of the tile. On tile that large better bounce twice on each. Properly laid tile will make a nice "snick" sound, hollow tiles will "thunk". You'll hear the difference right away. Keep track of your "snicks" and "thunks" on paper and figure the percentage of bad tile. If it's too high, it's a do-over.