Did you log out in your base? Logging out in your base puts you back where you were when you entered the base, even if you entered by a base teleport power instead of the blue base entrance.
Logging out while in a mission will put you back in front of the mission door you entered from; you don't stay in the mission.
Logging out near a mission door (and I use the term "door" loosely, since holes in the ground are sometimes "doors") will have you log in and animate coming out the door, and you'll be mooved a few feet from where you actually were to the door's exit location.
Beyond that, you shouldn't be moved after logging out.
http://www.fimfiction.net/story/36641/My-Little-Exalt
Note that "near" means "straight-line distance". You can log out on one side of a wall, and log in coming out a door on the other side, or in one case, log out aboveground, and log in while falling to your doom beneath Peregrine Island.
Now, that said, if you log out standing in front of Positron and when you log back in your in Atlas... Somethings wrong.
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Occationally I noticed logging out at the market will place you out back, with the door animation, when you log back in but it appears random. No big thing but it's a tad disorienting if I hadn't played that character for a while since I always park them somewhere to earn a day job badge before logging.
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When in doubt, change your password. It's a good idea to do so from time to time anyways.
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--The Question, JLU
Quick question: Is it normal to log back in from a spot that you did not log out from? This has happened twice and was just wondering if possibly my account has been compromised.