the "teens" dates all the way back to 1673: Your poor young things, when they are once in the teens, think they shall never be married. (WYCHERLEY Gentl. Dancing Master). originally, teen was almost always used in the plural in phrases such as 'in or out of one's teens'.

"teen-ager" originated in the US around 1941: I never knew teen-agers could be so serious. (Pop. Sci. Monthly) [where 'teens' would have sufficed!]