In Blender 2.90, this problem no longer exist as far as I can say after some testing:
Screenshot after having manually entered frame number 11 for the playhead positioning which caused a recalculation of the "Arm Spline" lagging behind the "CTRL_IK_hand.L" bone in Kent's demonstration up to video mark 10:17. The "Extra Object Update" and "Extra Data Update" functions which the Blender developers had introduced as a hack for updating the "Dependency Graph" at every frame (see video around 10:30) have been removed:
Nevertheless, I'm wondering when this issue has been resolved?