From a historian's viewpoint, I'll just mention that people have a great tendency to assign cyclical or repeated, connected titles to things that happen. For us, it's often naming something a revolution, be it during it happening or in hindsight. Or giving different times arbitrary names such as "the middle ages" or "ancient history." For Eorzeans, the same could be the Calamities, and the Astral and Umbral Eras.

So essentially, it could just be people saying "Eh, this looks like a calamity, which number are we on again? Seven? Ok, the Seventh Umbral Calamity just happened."

To go with this, our current, seventh, Astral Era supposedly began when we Warriors of Light beat Baelsar and Ultima Weapon. And who decided that it happened then and in that way? The leaders of the city states. Politicians. People who could use the morale boost the people get from that.