Zoomed in, that second picture has a smeared edge. Looks like some kind of vinyl and not solid wood.

What indicates that is thick solid wood for the top layer? It could easily be pressed super thin veneer like they would use on simulated raised panels.

The adhesive is irrelevant as far as warpage caused by an imbalanced panel. Meaning it doesn't matter. It will warp or not warp, regardless of the adhesive used to bond the outer layer.

To answer questions:
Rich C I have actually laid eyes on the tiles from the first two photos. Definitely solid wood 1/8" +/- adhered to baltic birch ply. Regarding the pressed veneer possibility, in watching the installation video I can definitely see a thick wood edge on the tile, and the wood grain transitions from face grain to end grain as the 3d relief is carved (more visible on the acute portions of the 3d relief) which wouldn't be the case in pressed veneer. Perhaps I'm wrong, but I do a fair amount of 3d wood cnc fabrication so it does appear to me to be of solid wood.
Adam Fair point. I wasn't sure if there was some trick regarding doing this ( using compressed wood, baltic birch ply is strong enough to resist cupping) or, if this is solid wood as I am supposing, are they just culling any tiles that bend after gluing and hoping for the best. Thanks for the input.

It doesn’t do you any good to use the best glue on Earth, when the glue line of the face veneer is where it will fail.

Total panel thickness is 30mm. Looking at the installation video, it appears that the ply substrate is much of that thickness - at least 3/4". I think they are just gluing the solid onto the ply and hoping for the best. Not what I would do!

Funny that this post would come about today. Yesterday I had a customer come into the shop with a 38 inch by 38 inch piece of maple 1/2 plywood with 1/4 inch quarter sawn white oak glued to the maple. The pattern of the white oak mimicked old parquet flooring. He only wanted us to square the panels on the cnc. I questioned the method of gluing the solid wood to plywood and having opposing grains. He stated that he has been doing this for many years. He does commercial flooring in large commercial buildings.
As I looked at the glued up panels, I could only see failure (from experience) but he swore he never had a failure in more than 7 years of commercial flooring with this method. I just scratched my head and still can't understand it. I wish the "Wood Dr." would have been there to see it. Still scratching my head.....

Limit the amount of moisture introduced to the panel in the glue up which essentially pre-expands the veneer at glue up - then your face just becomes another ply - albeit a thicker one. All of these examples are relatively small - the mosaic tiles just don't have enough dimension to cause a significant deflection, the black tile has grooves routed through to break up the face tension, and the 3D example has z height to counter the warping force.
In my experience, cupping problems occur in the shop when the layup is fresh out of the press and exposed to different drying on one face to another.
Site warping issues have been from predictable causes such as flooring laid on fresh concrete. I'm sure the installation instructions for these products have a caveat for poor install process.
Engineered flooring (sorry David, that's what they call it) does this all the time - a thick veneer prefinished on one side not a balanced panel.

Thank you all for your responses.
Keith. I agree that all of the cumulative knowledge and experience of the woodworking world would side with you (myself included), and yet these companies are making and selling these products. The company that makes the tiles from the first 2 photos has been doing this for 5+ years. I have been aware of their product line for most of that time and have been speculating on their imminent failure for years. I agree that is not a lifetime in terms of track record, but if the product was that faulty, I would think they would no longer be in business by now.
Paul: Agree but I'm starting to wonder.

Thomas: Thanks for posting. I could see how parquet might be more balanced with grain in opposing directions, but still a valid example. Curious if you know what type of glue he used?
Tom: Thanks. I have seen plenty of engineered flooring that is pretty similar to these examples. Maybe not quite as thick a 'veneer' but still they make some flooring that can be refinished which is usually 3/16" thickness. Good points about how each tile has some characteristic that will minimize cupping.
So........ Back to the original question. If you had to speculate, would it be Epoxy (West marine or system 3), Urea resin, or good old titebond 1/2/3? Thanks everyone! This post has gotten nearly as many responses as my 'who are you voting for' post last year.

I think the top photo (multi-faceted pyramid) is simply a moistened standard paper back veneer vacuum pressed onto the shaped substrate. Can't say for certain this would be a reliably repeatable process but it is where I would start if I was trying to duplicate the end product.

I would think the lower two photos have individual veneer components in the 3" to 6" wide max. range. I would try TB2 for that process as each individual veneer segment needs to move independently and TB2 as good flexibility characteristics. The wood movement on each individual veneer component is so small I'd think the overall product would hold up.

BH Davis

Just guessing but if I were to try this I would have the shop use UF glue. I would choose not to be there on those days because I get a constricted throat from UF exposure.

Unbalanced panels are caused by two things. Having one completely different product bonded to onside of a stable(flat) panel. The other is moisture permenance. If you coat one side of a panel with a moisture resistant product the panel will warp/cup a very high percentage of the time.

It can be hard to ascertain as to which is happening. For instance when using regular thin veneer you are coating one side of the panel with water perm resistant glue. It should cup. If you coated the other side with epoxy resin(0 perm) would it still cup?
If you did the same test but used 1/4” solid veneer would coating the opposing side with epoxy balance the panel? I don’t believe it would.

This is where experience & test panels & Woodweb can be helpful.

Thomas, 1/4 sawn does not expand in it's width, but mainly in it's height. I can't say if the plywood will stay flat, but good chance it will nailed down to floor joists.

Wood moves (warps) in response to changes in the RH in the environment.

Increase the RH, and the solid wood will expand a bit (see "Shrinkulator"). If it is bonded to plywood or something that does not respond to the change in RH, then it will try to move. The smaller the part, the less potential for movement. Larger panels will show problems before small parts do.

Y'all need a re-reading of Bruce Hoadley's Understanding Wood.

I’m waiting for

David Sochar’s Understanding Wood

Hoadley’s book is good, but a bit dated at this point. We need the Bible part 2. People have been doing all kinds of different things with wood, woodlike products and epoxy resin, since Hoadley

Re-reading your question, you seem to be thinking about the secret glue only real woodworkers can buy. You don't need it. Conventional glues will work fine.

Your objective is to glue veneer down so it does not move, so you want a rigid glue line. Easy enough. We do not know the depth of that object in the photo. If it is only 1" or so deep, then a membrane press would be used to press that veneer in place. Mass produced veneer panels get the veneer applied in membrane presses.

If the object is much more than an inch or so thick, then I think we are seeing 5 pcs of veneer carefully applied to a built core. Or 5 pcs of veneered substrate.

I would veneer a substrate (with backer if possible), then cut it apart, bevel the edges and put it back together again, taking great care to match grain. Rift would be best, if you have a choice.