I missed this thread earlier, so now is the time to acknowledge all the previous work, before I attempt to handwave a consistent, and hopefully realistic story.
For this analysis I will assume that the plastic bags are impermeable barriers to water, and we can extend that impermeability also, to atmospheric gasses.
The interstitial spaces between the particles of clay contain some water and some air. Clay is a phyllosilicate, each layer within the clay particle can store and exchange metal ions with the external water solution. Hydrogen and potassium ions tend to fluidise the layers and so break up clay particles. That ion exchange is not important here, as the clay provided for pottery, will have been stabilised, my guess would be that it is saturated with a balance of sodium and calcium ions. To be specific, water is adsorbed onto the surface of the clay particles, while ions are absorbed into the clay particles.
The windblown dust seen when cultivating arable land during a drought, is often dry clay particles, being lost from that soil. When water is first added to a dry clay powder, the water is adsorbed, with some air being displaced. That clay mix is unworkable as the particles cannot move relative to one another. Adding more water will take the clay to a state where the particles are lubricated by sufficient water to make the clay workable. Too much water and the product will flow away, the clay particles being suspended in the liquid water, like a muddy river in flood, flowing to the sea.
We know that the plastic bag of potter's clay was workable previously, but the clay has been exposed to the air, and has dried out to the point where it cannot be conveniently worked. As the clay dried near the surface, the spaces between the clay particles were back-filled with air. The block of clay has dried out in depth as some water has diffused from inside towards the surface. The entire block has then become firm, with the surface the driest, containing most of the interstitial air. At this point the water content of the clay has fallen just below workable, so only a small amount of water, maybe 10% by volume, should be needed to take it back to a workable composition.
First, the required makeup water is added to the firm clay in the bag. The neck of the bag is then tied, not sealed hermetically, but still sufficient to allow excess air within the bag, to rise and escape. The tied neck is orientated uppermost. At this point there is an option for a secondary bag, the neck of which will later remain above the water, preventing external water flowing into the inner bag, mixing with the makeup water and clay.
The bag is then submerged in a bucket of water. That places an equal hydrostatic pressure against the water in the inner bag, causing air to escape, and the full surface of the clay block to be wetted. As makeup water moves into the clay, more air will be displaced, that will rise to be escape through the neck of the inner bag. That ensures the clay is fully surrounded by water. The outer bag allows the neck of the inner bag to be below the surface, ensuring the top of the clay is wetted only by the makeup water.
Given time, the provided makeup water diffuses into the surface of the clay block, pushing internal water ahead of it to equilibrate, allowing the clay particles to be better lubricated and so, to be workable. That is why a big block of clay can be made workable in a couple of days, as the individual water molecules only need to move a short distance inwards. During that process, the air displaced by the water needs to escape the block, rising and hopefully escaping the inner bag. The external hydrostatic pressure aids in that buoyant process.
Anyhow, that is my understanding and explanation of the rehydration procedure.
The rounded dents in the surface of the clay seem to be a customary ritual procedure. After doing everything possible, the potter can then rest assured, leaving the process to equilibrate over a couple of days. I doubt the dents make a significant difference. They do increase the surface area slightly, but they also form irregular pockets, while their creation threatens the integrity of the inner bag, making the optional outer bag more necessary.