Well that is the problem exactly. The plugin tries to send the results to the results page to display the same ones as on the drop-down list. But there is a malfunction on the results page itself, so it has no effect on it whatsoever.
That is why I disabled the search to make sure it is not related, but even the native results page is showing random results. It completely ignores the search query. The search results page needs to be fixed first, so it respects the search query as it should, then it will resolve this issue as well. I’m afraid I don’t know what the cause is, but it is definitely not the search plugin.