The dock moving between screens is a Mavericks feature, rather than anything to do with DisplayLink.
Unless you mean it's completely random and happens even when you're not using the Mac of course, in which case it could be a DisplayLink issue (not one I have ever experienced).
Basically, the way it *should* work is if you put your mouse at the bottom of a screen, the dock will move to that monitor, if you do the same on another screen, it will move to that one, and so on; you'd experience exactly the same behaviour as this with multiple monitors plugged up via Mini DisplayPort, Thunderbolt, etc.
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