Was there a person who decided “Alright, we’ll start counting every hundred years from now.”?
The BCE/CE dating system is based on the Christian Anno Domini dating system, and its years are the same out of convenience. The idea of measuring years since the thereabouts birth of Jesus (not death) was itself a Sixth Century creation, attributed to the monk Dionysius Exiguus, who was attempting to calculate when Easter would fall. Until then Christians used various dating schemes, based either from the founding of this or that great city (e.g. Rome), or how many years into the reign of their King.
So, to sum it up: yes, the 1st century of the Common Era has Jesus' life in it for a reason - because they copied a popular holy calendar based around his death.