If you add a pdf to a new, still unsaved/unpublished post, and then save/publish the post, you will see the problem! In your screen recording I think you add a pdf to a previously saved/published post. Therefore it works.
But maybe there is no way around this problem, except informing the user to save the post before adding the pdf? Or is there a script that can save the post in the background as soon as the title is written, or something like that?
The problem is, if the user forgets to save the post before adding the pdf, the pdf will not be searched by SearchWP, until it is manually attached in Media Library.