Hi,
Well, without access this is going to be near impossible to debug, but I will try.
If I understand correctly, you have posts (or other post type), and some documents, that are attached to some of the posts. You want to find & display the posts, where these documents are attached to, while searching for the attachment titles? That is not possible in general.
The plugin can look for the attachments directly, display them, and make the attachment link point to the parent post – but the attachment is displayed, not the post that they are attached to.
The inconsistency could be explained as well – searching a certain keyword was giving you the results, but probably because of a match on a field in the post (description or meta or other selected fields), but not from it’s attachments.