PocketBib can download all of your linked PDFs so that you can view them even without an internet connection. By default however, PocketBib only keeps copies of recently downloaded PDFs.
To change this behaviour, tap the gear icon at the bottom of the libraries list:
Then tap "Local Storage":
And finally "All Linked Files".
There is currently no user feedback on the download process except for the spinning network indicator in the status bar. You will need to keep PocketBib open while it downloads your linked files, but the process will resume automatically the next time you open PocketBib.