I don't have ancient references, but my best understanding is an interpretation from Schoepenhauer:
Mathematical necessity, according to the principle of sufficient reason of being, in virtue of which, every relation which is stated in a true geometrical theorem, is as that theorem affirms it to be, and every correct calculation remains irrefutable.
So I think you are right; 'circular' is formal. Take the example of a triangle contains 180 degrees. It is necessary due to the all the constraints in the representation; it cannot be otherwise, therefore what is 'responsible' for this is a formal idea (eidos, causa formalis).
However, I am guessing Aristotle is wanting to put a fundamentally empirical or pragmatic outlook to work on this. There is still debate over what exactly a generalized reference is (how it is or isn't related to the collection of representations it references), so it has not been settled.
Firstly, a geometric understanding of 'circular' contains a set of relations that must be observed and can take multiple appearances and representations related to the circle's being. What is it that you think about when you think of a circle? It might be its roundness (can you conceive it perfectly round?), or the proportion of its radius to circumference, a curved line joining itself, a plot of sinusoids, a collection of innumerable points, a highly symmetrical object. If you think of its symmetries, which of them? What size is the circle in your mind? In reference to what? Its position? The circle we observe or imagine is relatively not far from a form, but it is still a relation of finite constraints, and it cannot be represented perfectly. The circle will therefore have a 'logical necessity' as well as a formal one.
Any representation, drawn or imagined, will make certain concessions and could be considered simplified in some sense or wrong in some senses, so it is not the ideal form. It is represented by definite, possibly finite materials that at any rate describe it and caused it to be. Therefore, it has a 'material necessity'.
We have certain understandings of why a circle exists, in what context, where it comes from, what it is meant to achieve, what it reveals or is of interest, therefore it has a 'moral necessity'.