Personally I wouldn't touch a spiral cut blade with the proverbial barge pole, though I should say that some people swear by them (rather than AT them)! I think a lot depends on how much previous practice/experience you've had, and how (exactly) you learnt how to cut.
Personally I would only cut a circle like that, especially in thicker stuff, WITHOUT a jig, by free hand only. That requires some practice, though from what you said in your OP about "letting the blade do the work", suggests that you are indeed on the right track (sorry, no pun intended).
The problem with using a jig with some sort of centre "pin"/bolt/pivot>whatever is that your natural tendency while rotating the work is to have at least some pressure moving against/towards the centre pivot, i.e. there's at least some tendency to force the blade sideways (looking in the vertical plane). This WILL tend to cause a spiral cut, or, if the pressure is too great, will eventually snap the blade.
The ideal when cutting any line, straight or curved, is for the cutting force to be exactly ALONG the line to be cut, with no force at all tending to push the blade sideways in either direction (either in towards or outwards from the centre).
In other words, in the "perfect world", your blade will stay absolutely vertical with the job moving in a smooth arc into the blade exactly ALONG the line to be cut. That takes practice, and in my own case, even after a LOT of practice, I can't do it as consistently smoothly (with no vertical/sideways or backwards/forwards movements) as the experts you see on YouTube for example.
But I CAN do it OK sometimes, and like Arnold Palmer with his golfing displays of holes in one, "the more I practice the better I get"!
The same is basically true when it comes to spiral cut blades too (or so my own experience shows). One of the "essences" of the above-described cutting method is that the blade ONLY cuts when you move the job into the blade at 90 degrees to the cut line (give or take a little to allow for blade twist). And that fact of cutting at 90 degrees is in fact the "secret" to turning sharp right angle corners:- Stop moving the job forward into the blade, then pivot the job 90 degrees (or however many degrees you need, it can be more than 90) and the blade will NOT cut the job until you start moving the job into the blade again at the new angle. That's the essence of cutting a circle or any other regular curve - that continuous movement of the job into the blade because the blade will ONLY cut when the job's moving forward into the teeth.
But by it's very nature, the spiral cut blade is already twisted into a spiral by the manufacturer. That means that (looking downwards on to the job), there is NO angle that you can move the job into where the blade will not cut. On the contrary, whatever angle you move the job into, the blade will ALWAYS cut the job.
That's why I - and many others here previously have - semi-humorously - referred spiral cut blades as "the work of the devil"!
Having seen those posts I wanted to try for myself, so bought a packet of spiral blades, tried them, and found that for me anyway, those things are indeed the work of the devil.
BUT to repeat what I said earlier, there are other scrollers (many?) who DO use them and get great results, so if any doubt, a packet of a dozen spiral blades are relatively cheap, so why not give it a go?
But to go back to your OP. Personally, I would keep practising circles without a jig until you can do it.
Sorry the above is lengthy, but IMO anyway, there are actually quite a few different factors coming into ply when cutting circles, and again IMO only, one needs to fully understand what's actually happening to produce success - along with "practice, practice, practice".
HTH, good luck
Edit for a P.S. Assuming you're trying to produce a good result NOW (and practice does need TIME!) then I'd suggest that you try out the non-jig circle cutting as above, and if that circle needs to be accurately to size, and ROUND (!), then make sure you're always cutting OUTSIDE the line. Then take a scrap of MDF, ply, whatever is to hand, and make your circle jig but use it to SAND to final ROUND size. A belt or a disc sander does work well for this, especially if you haven't got HUGE amounts to sand off. Again, HTH.
. I've learned a lot from your posts.
, I have tonight purchased an annual subscription to this forum. Not even sure what I'll get out of the subscription, but very happy to say that in my short time on this forum I've already had far more than that value in guidance 
