Walking out of the circle doesn't affect whether or not you receive XP from the FATE. It's actually a pretty common tactic in higher-density FATE zones to leave a FATE around halfway to go on and move to the next.

Not receiving XP when you enter a duty is almost certainly not a bug; since the duty is on a different server altogether, it's not exactly practical to award you FATE XP when the FATE ends and you're in a duty.