AutosuggestSitelink currently reloads the page after adding a sitelink, but it should purge it first.
For example, when adding a category page on Commons it is usual to add {{Wikidata Infobox}}. A sitelink is then added via AutosuggestSitelink, but the page that reloads doesn't display the full infobox until it's been purged and reloaded again. The gadget should be able to take care of this.