Sephiroth did not kill Zack. Zack was wounded by Sephiroth and taken, with Cloud, to the basement of the Shin Ra mansion, where they were experimented on (this is where Cloud is infused with mako energy). They escaped together and headed for Midgar, but Zack was killed on the way.

Hsu has already refered to this scene. Check it out, it'll clear a lot up.