The millennials as an expression describing a group is clearly describing those who became active around the millennium as it seeks to describe a characteristic, that's something not often present in newly born. The "baby boomers" are a slight exception to the rule as it describes the time of their birth, but it only became a thing when they (ok, we) could do stuff and be identified as a group.
FWIW, I would take it as people born from around 1980 - 1990.