It appears that you're correct in that it's origin was here in the U.S., however, more specifically, it doesn't appear to date much earlier than the mid-1990's... This quote is a definitive as I can find:
"Dr. Geneva Smitherman, author of “Black Talk,” is distinguished professor at Michigan State University and director of its African-American Language and Literacy program. “When used by middle-aged and older members of the black speech community,” she informs me, “ ‘back in the day’ refers to the 1960s and often reflects a kind of nostalgic longing for a historical moment when there was a very strong black unity. . . . When used by members of the Hip Hop Generation, it generally refers to the beginning phase of Hip Hop Music and Culture, in the ’70s in the South Bronx. Hip Hop music of this period was more rooted in Black Cultural Consciousness, in contrast to the 1990s advent of ‘gangsta rap,’ with its emphasis on violence, misogyny and bling-bling.”
The Hip Hop Archive at Stanford University is directed by Prof. Marcyliena Morgan. “When ‘back in the day’ is used by youth to refer to Hiphop eras, there is no problem,” she said. “However, if an 18-year-old used it in reference to when he or she was 15, it is often considered preposterous.” “Ahmad (a rap artist ca.1994) in his song ‘Back in the Day’ reminisces about childhood, but also includes references to artists and clothes, etc., that defined the Hiphop era.”
Obviously a 'corruption' of "Back in my day"...