How to delete "Not you or want to join..for a different person"?
I think what you see when you have "other members personal details" that emerge is either because they are stored by your browser (so civicrm isn't involved, it's a browser feature) or because you are logged in as a user that has the right to see other members.

Try doing it without being logged in (eg. using the anonymous mode of your browser), you will see that civicrm doesn't show private information to anonymous visitors