It aired weekly (on Saturday or Sunday mornings) back during those years. I caught a couple of episodes a couple weeks in a row back in 1997 ( it was part of the fight between Goku and Vegeta). The timeslot wasn't the best so I didn't get to watch the whole thing until I started buying them on VHS in 1998.
I could tell it could be something special, it just needed a proper timeslot and a channel that could build on it. Cartoon Network solved that in 1998.
This is how I was first introduced to Dragon Ball Z in 1996. It used to come on Sunday mornings at 9 in my area. I don't remember The Tree of Might movie airing. Unlike the Toonami airings, the show ended with a Saban logo like this one: Saban Ent. logo.
Dragon Ball had aired a year earlier, but I didn't know it until I accidently came across it in an old TV Guide from 1995. The station had buried it at 5 in the morning on Saturdays where probably no one was watching it.