I've been really impressed with everything that has been done to build your house so far until I saw the wire mesh. Technically, wire is stronger then rebar at holding concrete together. Concrete will always crack, but the goal is to minimize it. Two ways to do this is using as little water as possible in the mix, and reinforcing it with metal, like rebar.
For the rebar to work, it needs to be on chairs so it's at 1/3 up from the bottom, to the middle of the slab. The same applies for wire, but since it's impossible to walk on wire while spreading it, the biggest lie in construction is told over and over again. We'll pull it up while spreading the concrete. And for the first half hour, they do this for pictures, but then they get too busy spreading the concrete, and quite pretending. I've seen crews where a guy was supposed to just pull up the wire, but he never makes it through the entire pour. Even worse, when they do play that game, and pull up the wire, they walk on top of the wire and push it back down again.
100% of ever slab done with wire ends up with the wire under the slab.
The main reason to use wire is it's easier. No tying, no bending, and a lot less physical work. Guys who do this also tend to add too much water to the mix. You have to be there to make sure they don't add extra water. Water creates volume, when that volume evaporates, you are left with a solid mass that has to deal with losing all that volume. This is why concrete cracks!!!! The less water it has to evaporate, the fewer the cracks. In a perfect pour, the cracks are all so fine and minor that it's almost impossible to see them. In a wet pour, the cracks can be massive!!!!
Cracking from a lack of compaction will take a decade to happen, and even then, it's pretty rare. Cracking from too much water is very very common.
If the concrete is flowing like liquid when they pour it, you have too much water. It should slump. It should pile up on itself and not want to flow. This is where all the work is, spreading concrete that doesn't want to spread is very hard work. Adding water so it flows easily is ten times easier for them. If you have a lazy crew, they will add water. It spreads easier, it finishes easier, and they are out of there sooner. The cracks will start in a few days, long after they are gone. And then you just have to live with it.