"There's a lack of distortion here, meaning the ruler's control over this area is weak."
Safe Room is a room in Persona 5.
"This place is another reality that the ruler's heart projects."
The dungeons inside a Palace are unstable because of the owner's distorted minds. Safe Rooms are places that are stable; free of any Shadows. The protagonist can consult party members, save in their games, and fast travel to other Safe Rooms or the Palace entrance.