The Twentieth Century begins with tweaking and developing the great inventions of the last century. Hence we jump ahead a few years. Adding color to motion pictures begins in the 1910s, but Technicolor (as a trademark) takes another decade.
Tommy & The Greyhounds are actually emphasizing something culturally significant in “It’s a Technicolor Christmas When You’re Jewish.” See, the cinemas are more empty on the 25th of December and some (chosen) people get them all to themselves. Ragtime folk fun.