All good, take your time.
My primary reason for thinking it’s definitely not is somewhat intuitive, based partly in what the term “nuclear” usually connotes, rather than just its strict definition.
Usually, I’d expect a “nuclear” reaction or process or whatever to have something very important to do with the specific elements (not compounds-- too big; not sub-atomic particles-- too small) involved-- exact atomic number, that kind of thing. One element decays and divides into others, or else fuses and combines into another. Maybe there are exceptions, but that, to me, is the essence of a nuclear reaction: elements changing their atomic numbers by various mechanisms to become other elements.
Antimatter, as far as I can gather (partly from reading xkcd, etc.), is basically just like matter-- except that touching any very substantial amount of it will give you and everyone near you a bad day. Anti-hydrogen is just like ordinary hydrogen; anti-helium, as I understand it, seems to behave like ordinary helium. (Of course, we haven’t had all that much opportunity to play around with it in large quantities.) If I’ve got this right, probably we could expect anti-uranium to decay just like our uranium, anti-plutonium to act just like ours, anti-astatine and the anti-transuranics to be just as absurdly unstable.
If antimatter of any kind contacts matter, though, what’s important doesn’t have a thing to do with atomic numbers, except insofar as those numbers relate to mass. Equivalent masses of matter and antimatter cancel each other out, no matter what kind of matter/antimatter they’re made of.
To me, that’s not nuclear, because it’s not related particularly to anything having to do with the nucleus. Maybe physics, as a field, says something different, but the differences in terminology I’ve been running into on articles about each suggest that they’re close enough to share a lexicon, but far enough apart to have different jargon.
My actual area of expertise is more in the humanities-- and the use of language in particular. (English major, then lawyer.) To me, swathing two possibly-related topics in different technical language implies a desire to avoid confusion-- that is, to make sure nobody thinks you’re talking about one, when you’re actually talking about the other.
This is admittedly based on an impression, not an exhaustive survey of the surrounding language (I guess in the sciences it’d be called a hypothesis), but it seems to me like they’re neighbors who don’t want deliveries getting made to the wrong address, so to speak.