Did the contractor installed the new layer of cement flooring correctly?
Rule #1 concrete cracks

Rule #2 you can't change Rule #1

That is why they put in control joints so the cracking occurs where you want it. Sometimes they come back the day after and saw cut the floor to add control joints.

Your pictures look like contraction cracks. These would not normally be a problem with a 4" slab but your thin topcoat could begin to break up if they get worse.

What kind of a warranty is the contractor giving you?