The concept of day and night has been a subject of great controversy, especially on worlds with multiple suns.
However, this controversy has nothing to do with a New Day on Improbable Island.
There are two likely sources for the term "New Day:"
1) It is a corruption of the term "Newbie" when spoken with a particular accent common to certain areas of NewHome. This is the story most humans stick with, although, as it makes the most sense, is the less likely of the two sources.
B) It is an alternate spelling of "Nude A," a legendary Kittymorph who yielded great weapons of mass distraction. This is by far the preferred story of the island as it is highly improbable and it gives Seth inspiration for his music.