Wire mesh in a slab is one of those things that I consider a no no. While in theory it's great, it's impossible to install properly. To work, it needs to be somewhere between the lower third of the slab, to the middle. To do this, it has to be supported and then not walked on. What they contractors tell you is that they pull it up as they spread the concrete, and in most cases, they will do this at first for pictures. Once the job gets going, they quit pretending, and focus on getting everything smoothed out.
Look at it this way, a 200 pound man walking on wire with a six inch spacing is always going to be standing on wire while working. It is 100% impossible to stand on it and pull it up into the middle of the concrete, and keep it there while walking on it. '
When the job is done, the wire will be at the bottom of the slab and totally worthless.
If it was my barn, I would either fire the contractor and find another, or tell him to remove the wire and use rebar.