Numerous Cracks in Poured Slab
Is this slab really the foundation? I'm aware of 'slab on grade' shallow foundations but I've never lived in a climate where that is practiced. In my region a foundation with footings would be poured first (even when there's no basement), then the slab would be poured inside the foundation walls. In this latter technique the slab is non-structural.

You also mentioned something about cables being tightened -- is this a post-tension concrete construction?

It's probably a good idea to have a conversation with your contractor about saw-cut control joints. Concrete will move and crack and will continue to do so throughout its life. 'Control joints' are so named because they [attempt to] control and conceal these cracks. If you have the slab cut then you get the opportunity to influence where the cracks will happen. For example, you can encourage the cracks to make straight lines and to fall in places where you wanted a grout joint. If a crack is going to telegraph through your tile floor, it'll be much easier to conceal or repair if it comes up in a grout line rather than crossing a tile.