Nick Petit

Not entirely sure what you're trying to achieve but there were a number of issues in the setup.
One big issue was the animation was done early on in the graph (a simple xform in Y) which makes the whole setup unnecessarily time dependent.
The main reason things aren't behaving as expected is you are then applying a transform pieces to the render geo only (not the constraints or the proxy geo).
The easiest way to fix the setup and improve performance is to move the animated transform just before the RBD Bullet Solver, and have it transform all 3 streams (render geo, constraints and proxy geo) at the same time by RBD Pack'ing the output of the RBD Configure SOP.
Here's an annotated version of your hip file that goes through a few of the issues and has the wall move upwards before getting hit by the collision sphere.

Generally, a good way to check the sim if it's not doing what you expect it to, is to visualize the sim geometry. On the RBD Bullet Solver > Visualization > Show Collision Shape. That shows the geometry Bullet uses in the sim (after the collision padding and shrinking is applied) and you would notice in your case it isn't moving upwards like the render geometry is.

If you look at the collision shapes for your concrete pieces they are rounded quite dramatically - decreasing the collision padding (you have it set to 0.02 on the rbd configure sop, try 0.001 instead) will help avoid small pieces naturally rolling around.
Same thing for the collision geo underneath - having smaller gaps between the pieces will help avoid small pieces getting caught in there on weird angles.

Your falling chest is solid, like an anvil, and with the material property set to steel, its total mass is not insignificant compared to the thin pieces of concrete it's landing on and compressing, causing some of that jittering. Try reducing the density if you can, otherwise maybe try increasing the bullet substeps a bit.

It kind of is working - internally everything is doing what you want, which is why the spheres are floating above one another over the lower bowl, and if you dive inside the rbd bullet solver, you can see the spheres changing into cubes.
The problem is the rbd bullet solver by default outputs what is plugged into it, transformed by the resulting simulation points. There are a couple of ways of achieving this, first by simply creating an object_merge pointing directly at the dopnet node inside the rbd bullet solver, or you can replicate the swapping outside the rbd bullet solver by tagging the rbd points that are being swapped (you add them to a "swap" prim group, you need to create a point attribute you can add to the attribs to output since we only use the sim points internally - no prims).

Here's an updated hip file with both options.