When and why did spandex become a part of volleyball?  

I have no idea.

In the early 90's is when it really hit volleyball.

Why? Well, it helps with mobility (the baggier the shorts, the more they get in the way of movement), as well as (believe it or not) coverage. Shorts tend to ride up or shift awkwardly when a player makes a dive or a roll. The player would then have to get up and fix their shorts. Spandex shorts are clingy, and don't hide much, but they don't shift, ride or slide down when you dive