Camera not being fast enough when falling was a conscious decision to play with feeling of unease and subtly discourage players from taking leaps into abyss. Still not sure if it succeeded doing that or it's simply annoying.
If you'd like to replicate our camera controller, take a look at Assets/Scripts/View/CameraController.cs on GitHub. Code is a bit messy, but basic idea is to smoothly follow player on horizontal axis and on vertical axis only when player hits floor/wallslides or moves away from vertical axis zone. You can enable debug drawing on lines 166-172 to see how it's working.