Hi!
Indeed, there was something wrong with the search there, but I managed to resolve it.
This was actually a tough issue to debug, but I found that the regular engine was working with that post type. I had to do a few tests on the plugin source on our local server to find out the cause. It turns out, that wpfd does actually change the mime type of the wpfd_file custom post type, however the index table engine did not expect that, as it is usually only used on the media attachments. The resolution was very simple, I just added the pdf and html mime types to the index list: https://i.imgur.com/TbEC0nB.png
And that’s it, the post type fields are now correctly indexed, and you should see them in the results.