Disconnecting either a J1772 or a Tesla EVSE works in basically the same way, electrically speaking, as outlined by
@Tesseract. The main wrinkle with J1772 is that you can unplug the J1772 handle from the Tesla J1772 adapter; but the J1772 design should stop the charging when you press the J1772 button, just as charging is terminated by pressing the button on a Tesla EVSE's (or Supercharger's) handle.
In either case, you can listen for the relay in the EVSE to click over and watch the car's charge-port light for extra clues and verification that it's safe to unplug. The light should switch to a pale blue when the car is no longer charging and safe to disconnect. In warm weather, it should stay locked until it's safe to disconnect, too, although you'll be able to unplug a J1772 handle from the Tesla J1772 adapter even if the Tesla's charge port is still locked, as will be the case if you unplug while the car is asleep -- but it won't be charging if the car is asleep, either. If the J1772 handle is unplugged when the car is
not locked, then the adapter will stay locked in place, at least in warm weather, to prevent theft of the adapter if you charge in public. Tesla had problems with the locking mechanism freezing last winter, though, so they've set it to unlock after charging is complete in freezing weather. Be aware of that when charging in public.
In sum, unless something's badly broken, there aren't any safety issues (to you or to the car) with unplugging. Videos like the one you referenced show how to most easily unplug a J1772 EVSE for convenience and efficiency.