Hi,
The configuration seems to be okay, that field should not be showing. I suspect, that there are probably whitespace characters of some sort in the field, and it is then still considered as “filled”, so it is displayed.
I cannot confirm that only by video, so if you can provide temporary FTP and back-end access, I will be able to check.
If not, well, then this is going to be very hard to debug, but you can try this change, in case it helps:
1. Make a back-up of your server files, just in case
2. Open up the wp-content/plugins/ajax-search-pro/includes/classes/search/class-asp-search-cpt.php file on your server
3. Replace it’s contents with this
4. Save the file
If there was whitespace in the contents, then this change will help.