So far on 'American Horror Story Freak Show', we have seen songs performed that were written by Fiona Apple, David Bowie, and Alana Del Ray. All of these songs from the last forty years, but none of them could have been around when Elsa's troupe of freaks made camp in Jupiter, Florida, in 1952.
So where did they get the sheet music for those songs from the Future?
I think they were part of a package (There will be more!) delivered by a renegade Time Lord known as the Meddling Monk.
The Monk is better known for trying to disrupt Earth's major historical events - like the Battle of Hastings in 1066. Most of his attempts created divergent timelines which had to be set right by temporal agents like Phineas Bogg.
But as the Tenth Doctor pointed out, History was made up of small moments. And so the Monk launched a series of temporal anomalies in hopes of causing a permanent disruption to the timeline of Earth Prime-Time. And the anachronistic music is an example.
(The delivery of Pepsi to the "Middle Ages" style kingdom of Camarand on the planet Mondas is another.)