Outdoor maps are weird for that. I don't think Escort is currently working, in the same way that when you Rescue Captive in an outdoor map, they just stand there. There's no "door" for them to go to. No idea if this is a bug or if that's just the way it is, sorry. 
Dec out.
I know some outdoor maps can be used for it, but I believe it requires some sort of exit object, aside from the glowy red square. A map with a truck or whatever should work.
If you mean the mission doesn't end, I've had the problem with the Traditional game. I've had to TP or SuperSpeed around and to the other side of the box to entice the escort to get close enough to trigger completion without zoning out myself.
If you mean you achieve your goal but the escort does nothing, it's because the AI wants a real door and doesn't have one on an outdoor map, and so, does nothing. We've told the Devs about it.
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Thanks for the help everyone. I think with this advice I can find a work-around.
I'm working on a mission where the player has to escort someone to the map entrance. The map is an outdoor map, however, and just has one of those glowing red areas that indicates the exit.
During testing, when I moved the rescued hostage near the exit, nothing happened. When I moved into the exit area, I zoned out, but nothing else happened. When I zoned back in, the hostage was waiting there for me.
Is there something I can do about this, or will I have to make an indoor map?
Also, I might as well ask now: the hostage is set to turn hostile when the exit is reached. Will the mission be complete when it reaches the exit, or after it is defeated?
Thanks for your help.