How did Albert Fink observe the tears?

According to Jeremiah Fink (Albert Fink's brother) in his Voxophone log, "Out of the Thin Air":

Dear brother, these holes in the thin air continue to pay dividends. I know not which musician you borrow your notes from, but if he has half the genius of the biologist I now observe, well...then you are to be the Mozart of Columbia.

The "Uncanny Mystery in Columbia" kinetoscope video* shows that some Columbian citizens have been able to observe the tears too. It also says that this has something to do with Rosalind Lutece's research.

These suggest that the tears appear in random places ("out of the thin air") in Columbia due to Rosalind Lutece's research on the tears and Albert Fink observed music coming from them. Jeremiah Fink has also been able to observe the tears to create some of the technologies that his company produces.

As you play the game, you'll notice that Booker and Elizabeth will notice music coming from the tears too. In one instance, they'll be able to hear the 1983 Cyndi Lauper version of the song, Girls Just Want to Have Fun through a tear and comment that they have never heard that song before. Notice that the beach music in Battleship Bay is based on the tune of "Girls Just Want to Have Fun". (As commented by @Kappei) There's also another tear in Finkton from which Booker and Elizabeth can hear Fortunate Son in its original version.