Pages not hidden from search autocomplete

I am working with a site and using your plugin. Thanks so much!

we have set a page to be hidden from the search results.

When you search for the page, it does not show up on the actual result page, which is good, but it does show up on our search autocomplete flyout functionality.

Does this make sense? (I can create a short video of the issue if it helps)
Have you seen this before?

Any way to suppress the a page from the search results AND the search autocomplete flyout?

Thanks!