Reading the OPs link it looks like that animation may have had some dramatic license. They are going to do two more mid coarse corrections on the way to “Mars” if I am reading it right. Of course the red planet won’t actually be there on the other side when they get there.

Also note that you can’t “fall into orbit” around Mars, at least not with this sort of trajectory and without an aero rake heat shield. A real mars mission would require a third stage reignition for Mars orbital insertion.