I haven't found any clues as to where the Fabricants' animals are from. I'm not talking about the cybernetic Fabricants but the animals without the metallic enhancements. I read at UESP that they are "synthetic". Are there any references to the whole of the biological part being synthetic or an actual creature? I no of no form of magic that can create creatures in the Elder Scrolls universe.
Synthetic would imply that they are totally constructed, which makes sense with the name "Fabricants." Sotha Sil was a wizard but he was much more than that, he has powers and knowledge that probably no other mortal has ever known all at once.
As for no "magic" that can create creatures, the Dwemer obviously were able to create robots that mimic life very well. Sotha Sil undoubtable would have studied them and went beyond. I think the Fabricants are just much more complicated and intricate robots. In the end, if you get small enough, robotics would probably appear just like life.
So, they are probably a combination of Dwemer tech, magic, and godly powers only Sotha Sil could have access to.