For me issues with Zivkovic are the same as Mousset. We simply don't use a style of play to suit either of them. Our neat (albeit at times ponderous) style simply isn't suited to pacey forwards.
Both seem to be the Plan B when we are either losing towards the end of a match, and we expect them to unlock an oppositions sat back defense out of nothing. Or when we are winning towards the end of a game and we look to stretch the game by punting it into the channels.
For me both could be good players for us, but we just at the moment don't play a system that suits them.
I'd definitely start Zivkovic against Southampton, give him a proper run out and see what he can do.