Possibly stupid question?

I had seen this movie back in the day, and after all those years, I wasn't remembering that it was set in the '60s. I was remembering of course the all famous end scene with "Time Of My Life", which was one of the most famous '80s songs, so I thought the movie was set in the '80s. And then I saw it again recently, and as soon as the movie begins, I realise that it's set in the '60s. And then I see the ending dance scene with that '80s song, and...I just wondered, how could these two people dance with an '80s song in the '60s? It doesn't make sense. I mean, this is not just a song they put in the movie, at the end titles or something, I wouldn't have much problem with that, but this is THE song that the characters listen to as they dance, right? A guy puts the record to play. So how can they dance with an '80s song in the early '60s?