Note that this only applies to Dwilight. Dwilight was opened later than the other islands and has a serious atmosphere, as well as seasons, which means the years have more meaning there than anywhere else.
In my experience other islands tend to use either the real world calendar, or the same with the years put 1000 years back (e.g. April 18th, 1011). It's just a convention though.
The game mechanics do not actually define years.