There is usually something called a sinking platform above the men. It has a monorail ring around the edge that the clam system runs on, a bit like a circular girder trolley.
The platform also has doors in it that the men only open when the kibble arrives down. This gives them protection from falling debris from the kibble etc.
The platform is suspended on multiple winch cables around its edge and can be raised and lowered. Obviously when blasting it is raised quite a way up the shaft.
There is nothing nice about shaft sinking work......