The musical style of Louis Lester's band, and especially the vocal styles of his singers and the sorts of songs they perform, are typical of the 1950's, not the 1930's.
Louis Lester is shown as a Black musician leading a racially mixed band. Though Black musicians were sometimes featured as special guests with white bands in the 1930's (Coleman Hawkins with Jack Hylton and Teddy Wilson and Lionel Hampton with Benny Goodman), racially mixed bands didn't become common until the 1950's.