No, these are not FEMA employees. The teams come usually from major population centers and may be from one city, or a group of cities/counties/districts.
When you have a collapsed building, like we have seen in Turkey, that takes an entire urban search and rescue team. So, our national capacity is 28 collapsed buildings. That is right, 28! Sure, a fire department could go do search and rescue on a collapsed soft-story, multiple-wood-floors building, but it takes specialized tools and training to undertake rescues in a collapsed concrete and brick building.
When I designed earthquake exercises I always put a policy-level decision in the mix that is a surefire way to get the elected officials feeling a bit weak in the knees. The situation is this: You have 10 to 20 collapsed buildings and only five teams allocated to your jurisdiction. Which buildings get teams? Schools, nursing homes, downtown high rises, hospitals?