Orlando, FL
The code - Uniform Building Code (UBC) - does not address slab cracks directly since these do not constitute a "life and safety" issue. However, the appearance of such long cracks so soon indicates that there is a real problem that should be addressed immediately before they build the structure and make it too expensive to fix. For starters, the appearance of these cracks shows a serious mistake by the contractor. There is no excuse for that and you should not accept them as inevitable.
Some of the basic guidelines they should have followed:
1. Use quality concrete - in your case at least 2500 psi, or whatever the plans call for. DO NOT add water before placing it - water weaken the fresh concrete and make it more likely to crack.
2. Create control (Contraction) joints as recommended by the ACI (American Concrete Institute). These are either formed during construction, or saw-cut soon after to a depth of 1/4 thickness of slab. A basic rule of thumb suggests to space control joints (in feet) about 2.5 times the slab depth (in inches). For example, a 5 inch slab will require joints every 12.5 feet. The resultant panels should be as close to square as possible.
3. Use reinforcement that is placed in the center of the slab. Most people still use wire-mesh, but rebars are a much better solution. If the reinforcement is not near the center, it may be useless in limiting cracks.
4. Provide wet curing. Concrete needs to be kept wet for as long as possible. Common recommendations is at least 7 days. When placed in hot weather areas such as Florida, the concrete may dry faster and start cracking within hours after placing. Curing can be done by covering the surface with wet burlap, plastic sheets, wet sand, or more commonly by spraying a curing membrane on the hardening concrete.
Missing any of these items can cause cracking. A contractor who fails to follow these guidelines is not following the best construction practice as recommended by the ACI. There are a few publications available from the ACI (through the online store on their website) - "The Contractor's Guide to Quality Concrete Construction" and "Slabs on Grade" are two of the best - which provide this information with the authority of the ACI behind it.
As for the "not to worry..." part. It usually means they either do not know better, or are trying to avoid fixing their mistakes. You should worry because these cracks will grow for at least another year or so and affect any kind of flooring you try to install. It may or may not get worse, but do you want to wait and find out after the house is completed and any repair will be very expensive and disruptive? Unfortunately, at this point when the concrete is still young, the only guaranteed repair is R&R (Remove & Replace) of the slab. Trying to patch the cracks is not a good approach since the concrete will keep shrinking and the cracks will reopen.
By the way, the plans should have specified the joints, reinforcement, and concrete quality. If the contractor simply followed the plans then he is only partly to blame. If the plans failed to specify that, he should have asked for instructions, or used the best practice as recommended by the ACI.
I would expect serious resistance from the contractor to any R&R demand. You may need to bring in an attorney at his time and prepare for a lengthy process. You will hear that "concrete always cracks" and that "every slab has cracks". The answer to the first is that this is why we have the four requirements above, and the second is wrong. One possible compromise would be to cut expansion joints in the slab today (using diamond-blade saw) and epoxy seal the cracks. That may minimize future cracking and fix the existing ones. But there is no guarantee.
Good luck.