peopleinside for others reading this discussion and to provide a summary of what was discussed in the GitHub issue:
The problem was between navigating to a page with the browser (full page HTTP request) and navigating inside of the page using the single page application (SPA) route (Mithril component with background API requests).
At this time this extension only covers full page HTTP requests. Supporting errors inside of the SPA navigation would require a lot of work and happens very rarely, at least with core Flarum and extensions.
But this does mean some links to users or discussions created by extensions will handle 404 errors with the default behavior (red popup in bottom left) instead of the full page customized error. One such example is the FoF Split extension showing you the links to splitted discussions you might not be able to see.
It's exactly in the same way Flarum has two different ways to show a 404 error in those two situations (full page with back to homepage link, or red popup), and we only customize one of them.
By analogy, this also applies to customized 401/403/500 errors. If they happen when loading a fresh copy of the page, the customized HTML code will be shown. But if they happen as the result of navigating inside of the SPA, the normal Flarum error popup will show up.
