I do not understand this Latin though; though it's part of the official name. “puella magi” in Latin would mean "girl of a magician”; “magical girl” would be “puella maga”, whose plural would be “puellae magae“; “puella magi” is singular, regardless.
Googling “puella magi” results only in things related to Madoka, so I'm to assume they simply got the Latin wrong.