Incorrect. Rested experience only affects the killings of NPCs, double XP as a part of this promotion affects literally everything (space, quest rewards, PvP, etc). Technically, this double XP is way better than what you would normally get from rested.
Then, as I listed above you can increase those benefits through boosts and Legacy perks.
But if you have rest xp built up, which takes over when killing mobs? Do we use up the rest xp then it goes to event xp, or does the rest xp stay "banked"?