I think we over-imprison people, but let's not ignore there was an actual crime wave. Between, say, 1960 until the peak in 1991, violent crimes per 100k per year went from 160 to 758 for a 470% increase, remaining over 600 through 1997. And even in 1995 nobody knew that the crime wave had peaked; it would take another 8+ years (6 years of data plus reporting lag) for people to realize that.

There's no way not to have a large reaction to such a dramatic increase.

my plot from the wikipedia data available [1]:

http://imgur.com/H2ahd9y

[1] https://en.wikipedia.org/wiki/Crime_in_the_United_States