1. What happened
The first time I edit the timing of a key in the Dopesheet, the edit is not registered. You can see this by swithing to the Curve view after the first edit. See attached video

2. How we can reproduce it using the example you attached
Open project
Open test scene
Open AW
Select mangagirl GO
Click and drag summery of last keys and move then in time
Open the Curves view... keys have not been edited

This only happens on the first edit after selecting the GO.