Your understanding is correct, when failsafe/RTH initiates the Phantom will first ascent to 20m above the recorded home point height (if it's not at that height or above already).
There is a way to adjust what the Phantom uses as home point (including the "starting height"):
-First, IOC must be enabled beforehand in the Assistant software. If you have P2 this will require switching to NAZA mode.
-After you first take off and the Phantom has recorded it's initial home point, fly directly above you to the height you want to reset the home point to (say, an extra 20m to give margin for the trees), and once you hit that height go into a hover.
-Flick the left switch between "off" and "HL" several times, and you'll see the fast green LED sequence indicating home point has now been re-established at that new height and position.
Now when it tries to fly home on it's own, it will first make sure it's at 20m above that new home height, or higher.