This can easily be tested with the Rigify addon: Drop a Human metarig (that has fingers) Generate the Rig
Select the base finger control on any finger (1st control) When you rotate in X axis, the entire finger curls because the subsequent 2 controls are set to Inherit Rotation. (Under Bone Tab > Relations ...) When you rotate in Y or Z axis however, even with the Inherit rotation on, the subsequent 2 fingers do not bend like the do in X.
Now try turning off Inherit Rotation on all finger controls. Select the Base Finger control again. Rotate along X axis, this one behaves as expected, the base rotates but the subsequent 2 controls are just acting like Children Of. Which is best. When you rotate along Y axis however, now the subsequent 2 controls counter rotate to preserve their initial world space orientation.
Am I missing anything or is this intended behavior ?
This happens regardless of whether rotation is set to Quat or Euler.