Starc grassed the catch, simple as that. He never had full control of the catch because he was always off balance in the process of claiming it. It is the same as when keepers spill what are initially clean takes because the impact of their bodies hitting the grass causes the ball to pop up out of their gloves. Exactly the same situation. An initially clean grab means nothing until your body is stabilized.
The sad thing is the bully boy tactics of Starc and co pretending it was legitimate and then acting like this great injustice has happened, holding their heads, etc. It is more like their egos can't take the video footage proving it was grassed.
It is hard to say but I don't think there would the same outcry if Stuart Broad or Ollie Robinson grassed one.
Australia handled themselves very poorly but it is not the first time they have found the laws of the game hard to grasp.