Turning on a unicycle can be a very clumsy thing.
Turning option 1
You basically contra-rotate your body under your rotating arms. It can be quiet a jerky action to have the desired effect if you are turning a sharp left of right.
For a while this is how you will do any turning other than meandering. It is also pretty much the only way that I know works on a giraffe.
Turning option 2
You turn by leaning into the direction. Just like on a bike, on a skateboard, on skis. And it is the one to use for gentle meanderign and follosing a windy path. But, other than gentle banking, if you rely on that on a unicyle then the turn will be fine for only part of it. Further into the turn you will pick u p wheel speed VERY rapidly. Well before you have completed it you will need to do a violent correction, wresting back control using a real heavy foot and grinding your rubber hard into the road. (Don't ask me exactly how the correction works but it seems to come naturally to everyone, no-one teaches you how.)
Turning option 3
For most turns at a range of speeds and especially where you need to thread a fairly exact path you should instead rely on the shape of the wheel to do the work for you. If you lean the uni to the right then you will be tracking on a right-hand curved track and will turn. However, what I have just describe is really the same as option 2.
However, you add one thing - you maintain your centre of gravity (CoG)more or less where it started - not to far away from the centre line - shifting your CoG in the direction only enough to compensate for centripetal force. You do this by piking your body to the side opposite the direction of turn.
For example if you are turning right then you lean the uni to the right (quite a lot if you want a sharp turn). At the same time you you pike your body to the left.
All these turns work and all are appropriate to certain circumstances. Indeed in any ride you will use them all a lot. However I see many riders who never realised the third option. And if you are riding around and within small spaces, busy peds etc then it really should be your default turn. The others come out only as required.
Arms out wide??
All turns have a degree of counter-rotation. But it does not have to be obvious or ugly.
Where you are seeking to use your arms for counter-rotation, I find that I no longer spread them wide. Rather, if I am turning, say, right then I will have my right arm trailing behind and my left arm out front, but NEITHER extending beyond my natural shoulder width. A bit ike parade marching. I then simply bring the arms back to my side and, as far as need be, beyond. So both arms could wind up being opposite where they started.
In conjuction with a bit of help from rotating my hips to transfer some turning moment thru the pedals, I get a clean smooth result. Nothing jerky and largely unnoticed by observers. And easily controlled and adjusted as I progress thru the turn which makes it the ONLY good option that I trust when I am negotiating a path thru moving crowds in typical city space.