When should I put the casing into the fruiting chamber?

Once the mycelium appears in the valleys of the casing layer, meaning you can see mycelium strands beginning to poke through the casing layer, but the surface of the casing is not yet colonized, you should initiate pinning.

The more evenly the valleys of the casing are colonized, the more even of a pin set you will produce.
The mycelium usually continues to grow for a few days further into the casing layer after the pinning has been initiated depending on strain. Some strains of Psilocybe cubensis are more aggressive than others (Puerto Rican mycelia has been reported to be quite aggressive, and some initiate pinning more quickly than they would for other strains of cubensis) . There is no set time, you must just judge for yourself when the subsurface of the casing layer is adequately permeated.

You initiate your casing when mycelium has peaked through the surface at multiple points seen around the entire area of the casing surface. This increases the likelihood that the mycelium has colonized throughout the subsurface layers of the casing layer. You want the casing soil to be colonized, but not the casing soil surface!
Look at the PICTURE in TMC of the large bulk tray of pasteurized cased straw. You won't see any mycelium at the surface of the casing, ONLY FAT SHROOMS.

You wait for the mycelium to PEAK out at multiple spots, to know that it has PROBABLY made its way up to the surface everywhere, but not on the surface.
If you can consistently lay down an even casing layer upon an even substrate, and you KNOW how long YOUR particular strain you are growing takes to colonize right up to the surface, but not on the surface, INITIATE BEFORE it comes out on to the surface.
Wait to see some surface colonization, peaking out, if you don't know how long it takes!
So the more you know your strain(substrain) the less mycelium you need to see on the surface of the casing layer!

But again, you want the subsurface layers of the casing colonized, NOT THE SURFACE itself.
If this happens, we speak of OVERLAY.

Overly is not such a big deal with Psilocybe cubensis, the casing will fruit nevertheless, but not as good as with a properly maintained casing.