The mune is forged in after the sunobe is formed and before the bevels of forged in. That way the full thickness of what will become the edge can rest on the anvil while the smith hammers the shape of the mune. It does not take lot of force to move this small amount of metal but still it would ruin the shape of the thin edge if done after the bevels are forged in.
It is refined later, as is the rest of the blade, with grinder, sen, files, stones etc..
Anyway, that is what I have observed from the few smiths I have worked with and do the same myself.