The confusion is this:
tip-toe generally means standing up on your toes. (ie, standing as high as possible with your heels off the ground.)
Now, tip-toeing pretty much only means walking around on tip-toes
tip-toe can indeed also be used to mean tip-toeing. Go figure.
So, you can say "tip-toe over here buddy!" you would then see Buddy tip-toeing over there.
Regarding the sentence in question, it's just very awkward and very bad. What are you trying to actually say? Do you mean the person is pirouetteing?
(If you do not know what that means, check dictionary "an act of spinning on one foot, typically with the raised foot touching the knee of the supporting leg.")
Do you mean the person is doing s "pique" on the spot? (Sort of tiny little steps as you spin around.) Do you mean the person has pointe blocks on and is on pointe?
A good tip for good writing is, I think, only use analogies in areas in which you are expert
For example: say I wrote "He was pulling back on the wooden stick, like a jet pilot pulling the joy stick in a banking mach curve...."
The problem is this: I have utterly no idea what a "jet" is, if jets have "pilots", if these devices have "joy-sticks" and if so what those are, whether or not you "pull" those, and I don't know what a bank, mach or curve is in an aircraft or if you use any of those in that way.
In the example at hand, I wouldn't mention ballerinas for any reason. It just sounds silly, you know?
There will be something in your field of experience and expertise, that writes a better analogy.