Wow, very interesting. I can't believe this is how a new house is built. Yes, hire a certified structural engineer and get a report. I am not one, but my degrees are in a very related field and my first gut reaction was "what the hell!" It seems totally wrong to me.
You are right the joists are exposed to weather, and that is not good. But, even further, from a cursory look around the webs, in general this is not a common building practice (search floor joists embedded in stem wall concrete). Concrete absorbs water. The key structural members are in contact with the concrete. You might have tons of issues down the line (termites, rot, etc.). If those joists ever need repair, it is a big hassle. Yes, there is some protective paint, but that paint can always chip off down the line.
Typically the joists sit on a sill board on the foundation wall. Yes, that wood is in contact with the top of the concrete, but much less of a load carrying member and more of a barrier. The tips of the joists are then covered with a perpendicular running board. Then the outside is covered with siding down below the where the boards sit.
How were the other houses built? It is possible they were built with the same joists in concrete, but they stopped the joist an inch or so away from the edge and were covered completely? Or they have some other covering? I highly suggest figuring this out (maybe even with the structural engineer). If they were built completely different (the proper way) then this is a huge problem for you.
Best case is that this method of construction is okay by the engineer, and all you need some protection from the elements. That might involve some kind of covering on the outside. The builder would hopefully cover that addition.
Worst case, this method is unacceptable and should never have been approved (or was not even what was approved on the official drawings by the city). You will then be hiring a lawyer as this is not an easy fix. Your builder/warranty will push back.
Worst-worst case are all models are built like this and it is all wrong. Then, this likely means class-action lawsuit (I've seen this a few times).
I am hoping for the best case for you.