Hi!
Thank you very much for the proper details and the video, it helps us tremendously.
That option does not affect the filter, it is only to set the keywords logic, entered into the search input field. I believe I understand what you need, you want a filter that is restrictive the more checkboxes are checked. There is an option for taxonomy terms to work that way, but not for pos tags yet (I see you use post tags).
However, with a custom code, it is possible to enforce this strict logic, so that all terms selected in the checkbox should match, but the unchecked ones are actually ignored (otherwise overlapping items would be excluded).
Add this custom code to the functions.php in your theme/child theme directory (copy from line 3 only!). Before editing, please make sure to have a full site back-up just in case!
This should get you very close to what you expect.