I’ve been seeing that Dorico manages correctly ‘curly quotes’ (’, ”) when you input lyrics, but not when you type text—using Shift+X—or in some predefined sets of text.
Here you have an example [Write mode > Tempo panel]:
The text shown both as part of the interface of the panel (see image 1) and inserted into the score (see image 2) uses ‘straight quotes’ (’, ") rather than curly ones. This is so annoying, and it also happens, as I said, when you input text with the Shift+X keyboard shortcut.
I hope you try to ‘fix’ this kind of typographic issue.