This is correct. The isolator above is also called "restrained isolator" or "seismically rated isolator". Many manufacturers, same concept.
The one to the left, below, is the other option, called "free spring isolator", totally acceptable if you do not have lateral loads or you have some other...
The 2nd part, about isolators, is for the mechanical engineer. In other words, any unit resting on springs needs to have snubbers. This is to avoid the unit bouncing around due to the lateral seismic load. It is the difference between the so called "free spring isolators" and the "seismically...
