Conclusion: Vixen's knowledge of how apostrophes are formatted is on par with Vixen's knowledge of their proper use.
Indeed, in addition to publishing notation-intensive materials, I've also laid out, typographically designed, and published ordinary materials for commercial print jobs, going back to the early 1980s. I've used a wide variety of typesetting systems, from desktop software-based systems to professional high-volume print systems. My father-in-law runs the offset print shop for a small town in Montana. The claim, "most formatting system insist in adding a space after either a single apostrophe or a double one," is patent nonsense. I have yet to encounter a
single "formatting system" that does this, much less "most" of them.
I wonder if she doesn't mean they add
some space (pixels), rather than adding
a space (the 0x20 character). That seems to be the only way to square her comment with the actual excerpts and screen shots she posted. Those don't have
a space between the “”. There are ordinary spaces
surrounding them; is the claim that those were somehow added automatically? This happens when you accept predictive text in some cases, but not for punctuation in my experience.
Yes, proportionally-spaced fonts on any modern computing device will perform some amount of kerning. This means when you type ' and " together, as in '", you're very unlikely to get a result where the kerning between the ' and the " matches the space between the two marks in the ". This is precisely why we have always approximated ‴ by using three single-quotes, '''. It obviates the kerning problem entirely and very quickly becomes second nature when you write a lot of mathematics.
Ironically the kerning for the actual typographical quotation-mark glyphs “ and ” tends to err on the side of scooting them even
closer to the adjacent characters.
In any case, even if take her statement as true, I can't see how this serves her argument. Regardless of whether some "formatting system" adds
some space (kerning) or
a space (smart text entry), it doesn't change the fact that putting ' and " together to approximate ‴ is something a mathematician or physicist knows not to attempt. And as usual we're hampered by trying to figure out what Vixen is trying to say through her gross ineptitude at applying proper or precise terminology.