I understand that inductor in this case is going to reduce the rate of changing current flowing through it, but I do not understand what is going to happen during the transient. Which device should react first?
The MOV is fast, but not as fast as TVS. So, initally the spike comes to MOV, but it doesn't react. The TVS "opens" very fast and begins to conduct. The inductor limits the current rate of change in the meantime the MOV begins to conduct and absorbs the large portion of the energy. Once the MOV begins to conduct, the TVS is unloaded, so it "eats" only the very beginning of the spike.