Hi Andrew,
The “asp_active=1” query parameter is necessary for the plugin to know to override the search results. If you turn off the results override option, then it will indeed disappear, but it will display the wordpress default search results instead.
I just checked, but I see the exact same results when the override is activated:
Ajax: https://i.imgur.com/bM9CK5u.png
Non- ajax: https://i.imgur.com/BjynHhM.png
In case I missed something, can you please also provide temporary FTP access? If the override is not working, it usually means that the theme itself is overriding the default wordpress search results, which is impossible to circumvent without touching the code.