I'm with rouxdoo on this. Sounds like you're using thin wire, which makes things unnecessarily difficult. 30 awg at the least, preferably 28 awg. The thicker the wire, the less likely it is to pop on you, and the less it will bite into the wick. Distributed pressure, etc.
Coil tension is key. One main problem many face at first is how fastening the coil to the center post affects tension in the topmost wrap. Try to look closely and pay attention to how it affects things. Depending on which way you wrap the coil around the post, it will either loosen or tighten the wire around the wick. Try to compensate for this by either pulling or pushing a little on the wick. If it turns out too loose, you can make a little kink in the span between wick and post to make it wrap around the wick more. If it's pulling on the wick, loosen up the screw and try again. This will become second nature after a while.
Also try to torch the wire before wrapping it. This will make it "softer"; making it easier to wrap, and help prevent it moving around on its own when subjected to heat.