First: We prepare commands for a voluntary action. This is done in the pre-motor cortex for actions that are reactions to external stimuli and the pre-supplementary motor cortex for ‘intentional’ actions. These commands are signaled to the motor cortex.
Second: The motor cortex executes the commands.
Third: Both the pre-supplementary motor cortex and the motor cortex sent signals to the parietal cortex, where the sensory consequences of the motor command is predicted. The pre-supplementary motor cortex signal give the sense of an urge to move. The motor cortex signal is used to create a prediction in the parietal cortex, the very near future projection of the movement in enters consciousness.
Normally, the conscious experience would be of a movement preceded or not by a sense of an urge to move.
However under the experimental conditions. If the movement is produced by direct stimulation of the motor cortex in a way that bypasses the signals to the parietal cortex the movement happens but there is no consciousness of it as the prediction is not made. If the parietal cortex is stimulated directly than the urge and/or the movement are made conscious without the movement actually happening.
So the result is not so odd after all.
The question of how free is free-will now is a question of the difference between the way that the pre-motor cortex and the pre-supplementary motor cortex initiate the creation of a motor command.