Well the point is that ä is one character, not two. It shouldn't be "a with two dots on it", it should be ä. It's its own letter with its own key on Swedish keyboards. MacOS apparently normalizes it to be two characters, and then somewhere in the publishing chain it gets mangled and end up as a¨. I have no doubt that it looked ok on the author's Mac.
It's been a while since I last saw it, but it wasn't because of the font since it was published on a Swedish newspaper's website and other texts worked fine.
A single Unicode codepoint could be represented in a couple of different ways (either decomposed into 2 or as 1). Assume it’s the single codepoint representation.
The font you’re using can (and probably will) rewrite it as 2 glyphs using the GSUB table. This makes sense because it’s a more efficient way to store the drawing operations. The GPOS table is then responsible for handling the offset to put things in their right place.
Main point is that it’s up to the font to move things about.
Now, that may not be what was going on in your case at all but it’s possible.
It's been a while since I last saw it, but it wasn't because of the font since it was published on a Swedish newspaper's website and other texts worked fine.