the way this works…..the headphone jack has a switch in it. When you plug the HF in, it opens the switch as long as it goes all the way in.
That either disconnects the speakers directly, or signals the circuit to turn off the speakers.
Therefore, there is no issue with the HF if they work. If the speakers continue to work then either the jack is defective if it is a direct switch, or the cutoff circuit is defective or a setting is wrong.
If there is anything in the plug, like hair or fuzz, that would cause the HF not to work. It would likely turn off the speakers since the switch would be activated if the plug went all the way in.