In the fall while the bed lies fallow for winter, immediately.
In the spring or summer near planting or with plants, compost it for 6 months as a general rule.
@gtaus - it sounds like you have a wonderful plan and set up.
I don't use a tiller, so take this for what it is worth. I've read comments that the tiller will disturb the ground too much and be detrimental to soil life. Try it, if you like the results let us know. Mixing the top layer in...
I have a slightly different approach. Same as you, I put wood chips, leaves, yard trimmings and kitchen scraps in the run and let the hens pick through them. I also have 6-12" of wood chips in the coop collecting all that goodness.
2-4 times a year, I will make a pallet compost bin (4 pallets...