So your mask needs to adjust over time. Don't most things in life? Not a problem. After Effects offers several functions for keyframing your masks. Let's get started by clicking the triangle by the Masks to open up the mask properties.
Click the Mask Shape stopwatch to set a shape keyframe. You can also press Shift+Option+M (Shift+Alt+M) to set an initial keyframe on a selected mask
Advance in the Timeline and modify your vertexes to make a new shape keyframe.
Make the workspace as long as your shape mask animation and RAM preview to see After Effects interpolate the shape transformation.
When modifying a Bezier handle, you will affect both the incoming and outgoing curves. To access one handle at a time, use the Convert Vertex Tool, and drag one of the handles. You can also hold down the Option key (Alt) to do the same.
If you want to rejoin your handles, use the Convert Vertex Tool to convert the vertex to linear, then back to Bezier again.