Basic Trope: A show or text set in the past uses popular, well-known songs as part of it's soundtrack.
Straight: A scene set during the 1960s uses a popular hit from that time on the soundtrack.
Exaggerated: The entire soundtrack is comprised of nothing but popular hits from the 1960s.
Downplayed: There is only one era song - but the one used is a popular hit.
These songs were popular and well-known during the period in question, and thus sold many copies and were frequently played on the radio and various other places where popular music is often heard. It's not unrealistic that the characters would have heard these songs at some point.
Certain songs are very good at evoking a particular mood, period or feel, which is recognized by a wide audience; the producers decided to embrace that when constructing the soundtrack.
The characters the story focuses on are stereotypical "hip" youngsters who constantly listen to the latest popular hits, and are more likely to do so than any other demographic.
Only very obscure songs from the 60's are used.
A song set in the 1960s that only references popular movies from that decade.
Subverted: A character turns on the radio, signaling a period hit to start playing on the soundtrack. Instead, what plays is a more obscure track, or isn't music at all.
Double Subverted: The character changes the station; on the new station, a period hit is playing.
Parodied: The character can't escape one particular popular period hit; it's playing on every single radio station at the same time, everyone is listening to it, and even places where you wouldn't expect to hear that particular genre of music (or music period) have started playing it. And the character hates that song.
Zig Zagged: The soundtrack features a mixture of popular and well-known hits, more obscure tracks and original music.
Averted: The soundtrack is made up of obscure songs from the 60s that no-one's heard of, and which may or may not have been popular at that time.
The producers were limited by the songs they had the rights to use, and decided to choose songs that at least people would recognize.
Lampshaded: "I keep hearing these same songs no matter where I go!"
Invoked: One of the characters is a music lover with a playlist comprising of popular songs from the period, and keeps playing it.
Exploited: A time traveling protagonist happens to wind up a musician at a 60's night dance. He plays the hit songs he knew to blend in and not reveal himself by playing obscure ones.
Defied: The producers make a conscious decision to select more obscure, less-heard tracks for the soundtrack, or hire a songwriter to compose original music.
Discussed: "I know these songs are popular, but you think they'd play something other than hits every so often!"
Conversed: "I know these songs are popular, but surely they wouldn't have been the only things anyone ever heard back then; you'd think the producers would at least try to include some more original stuff."