he uses the mesh to sub divide the envelope shape then watch how he drops the vertices down further (not the default sub divide) then he only edits the bezier handles for the lower portion that is bent.... any art contained inside the envlope shape is going to try to conform to its shape (when the bottom 'bends' it to bends... the top part literally has no curve so it doesn't)
play with AL the handles -- you see how they affect each other... when I pulled most of them in closer to the vertex pint seemed to dull the bump.Notice the ones that are horizontal... mess with those. and then mess with the vertical handles to get what you want. Tutorials are just starting points, you gotta play with settings until it is right for your file. Experiment 

If you subdivide it one more time than the tut did... gives more control... see below.
