As she says in the movie, it's just a metaphor for anything bad. The important thing is that she calls Trent Baba Yaga in the beginning, but then shifts to calling her dad and the security guard Baba Yaga at the end.

If anything, turks probably adopted that story from slavs. Turks actually conquered large number of slavic lands in 14th century, and they had this custom of kidnapping young boys and taking them back to turkey, where they would train them to be soldiers, so called janissaries. Janissaries actually enjoyed quite a standing in ottoman society. It's quite possible they brought the story along for the ride.