How is it that every decade has its own musical vibe to the point that you let someone listen they can tell you that song is from the 50s, 70s, 80s, and so on?

Music is pretty self referential. Someone comes along with a new idea (or often an idea copied from somewhere else). Other musicians hear that idea, like it, and do their own take on it. So ideas are related, but building on each other.

Then you factor in the nature of the music business. Specific songwriters, studios, producers, house bands, session musicians, engineers etc might be involved in a large proportion of the music of a particular genre/era. No matter who the headline group or musician was, often the people in the background were the same.

Motown would be a classic example. There were offices for songwriters, so they were all sharing ideas. A lot of the albums were recorded by the same engineers in the same studio. A lot of the backing musicians were shared. So of course there's a distinct sound to it.