That's because the year 1572 of the Sixth Astral Era is the year that the Calamity actually occurred (the year that 1.0's original storyline happened in, ignoring the Echo-jumping into the past that happened a lot of the time). Dalamud's summoning wasn't an instant event, it took time (essentially a year and a half of real time) before it finally came down resulting in Bahamut's release.

From that specific date the era changed to the 7th Umbral Era - which the general consensus is, by the time ARR starts, it is the year five of the Seventh Umbral Era.