As mentioned in today's review, Quasar was a fully fledged member of the Avengers. He officially joined the team in 1989's Avengers #305, when Captain America basically called every active and reserve member of the Avengers together at once and asked who would stick with him. So the new team roster was:
Gilgamesh got injured in a battle and was replaced by Sersi. Iron Man was in and out depending on his schedule, Vision and Black Widow joined, and then the next thing you knew it was just a hop, skip, and a jump to the "bomber jacket" era, when Quasar was off doing his own thing in space.
It's not the weirdest lineup ever (the team right before him included Reed and Sue Richards, for example), but the most charitable thing we can say about it is it was a "transitional" period.