You are correct. And from my understanding, the HP doesn't automatically "follow" your RC/mobile device when u do this, but records the new HP at the time you tap it. In other words, you have to periodically hit the "home" button to update your position.
I did some tests on Home Point Me and it appears that the HP used is the controller's position at the time the RTH button is pressed. If the controller moves after the RTH button is pressed, it still goes to the position of the controller when the button was pushed. Having said that, I have no idea what it does when RTH occurs due to loss of signal, since it is no longer in contact with the controller. I would assume (dangerous) that it keeps a running tab of the controller's position and uses the last known position if signal is lost.