Ok, short answer is… I have no idea. This looks like a bug! I can’t get it to work as expected. I think it’s worth reporting to the developers.
There is a workaround though. Head to the action editor and choose your pose library as the action you’re viewing. Each pose is associated with a keyframe. The first pose in the list is the first keyframe, the second is the second keyframe, etc. If you manually insert the keyframes on the proper keys, the Apply Pose button in the pose library will work again. So, the bug must have to do with the Add Pose operator not respecting all of the bones. I can’t find any reason why it’s not.
If I try to use the pose library in a new file with a fresh rig, however, the library works as expected.
Oh and nice model BTW 🙂