Hi,
I think the problem is, that there is a mod_rewrite or functional redirection to the results page. I see the plugin trying to redirect to the results page, as https://www.kemiko.com/?s=phrase but it is automatically converted and redirected to https://www.kemiko.com/search/phrase
This causes the query arguments not to pass along, and the override does not kick in. I would suggest trying to change the redirection URL, to custom, and entering this there:
search/{phrase}?asp_custom=1
If there is no further redirection forced by the the .htaccess file, or any othe function, then this may work.