Almost every calendar system has a similar trick: https://en.wikipedia.org/wiki/Intercalation_(timekeeping)

The west inherits from the Romans, and Julius Caesar standardized away the Roman intercalary month by glomming it into Feburary. Before that a "priest" (the pontifex maximus) (in scare-quotes because it was a political office) would add that month on an ad-hoc basis. Not so different!