Nope, even experienced brickfilmers can still have trouble with this. I do.

I typically grip it by the face, and by the back of the head/hair, and make sure my grip is extra tight. That helps to prevent them moving separately, but even that doesn't always work. If you can, try gripping just the head and turning that. The hair should come along for the ride, and if you didn't bump it, it shouldn't move.

As for securing it better, you could try placing sticky-tac between the hair and the head. But not too much, otherwise the hair will stick up abnormally.

Here's what I do:

First, place the head on the torso and twist it around both left and right.  Doing this for a bit will begin to loosen up the head and neck.  However, this will not make it too loose, so you shouldn't have to worry about that.  This will make the head more more easy to spin.  I always loosen up a figure's head before I use it in animation.

Secondly, use some sort of sticky substance to stick the head more firmly to the hear or hat.  This is especially essential if the character wears a full helmet which still reveals the face.  I use a substance called a kneedable eraser.  It's usually used for drawing, but it's useful for animation since it never dries out and doesn't leave residue so long as you dab where it's been with a tiny wad.

Finally, you should be able to turn the figure's head quite easily.  However, as a precaution, it would be well and wise to go ahead and try to hold on to the character's face rather than hair just in case  the sticky fails as Pritchard suggested.

For me, it always works best to push down on the hair or hat and turn that way. Usually, the head moves with it but you have to put something sticky in between the two pieces. It also does not work for every shot because it may move the torso. Even though it has a lot of problems, this method is very handy for doing simple shots very quickly.

Some people are horrified at the thought, but I sometimes sand down the torso necks until I can turn the head and hair smoothly as one. Some torsos are old and worn enough that they can do this anyway. Another method is use is pinching the head at the base under the hair and pulling it up while trying to turn slightly, then pushing it back down. This means not having to remove the hair. Also, don't feel bad about having difficulties with head-turning animation; it still annoys me often.

How much is a little?

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Well, sanding down the neck didn't really work, but I may not have done it enough. Luckily though I found a trick to line up the minifigure's hairpiece.

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This is my method, as well. As Squid said, this will successfully loosen the head without making it too loose.

I don't ever use sticky tack with hair. I just firmly grip the head and turn it carefully. If the hair slips, I toggle back and forth between frames and "eyeball" where the hair was originally, in relation to the face. This gets easier the more familiar you are with a particular hairpiece or faceprint.

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I heard from someone else that using a tiny bit of sandpaper inside the head does wonders. Seems safer than a drillbit.

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