Here's how I did it, and you can only do it manually

, from what I can tell.
- make sure that the check box in Tools/Options/Storage is checked
- open the email with an attachment
- touch Edit/Mark for Download (it should now download)
- wait until the green arrow next to the attachment disappears
- touch the attachment file name, and it should open in the associated program
That's it! Manual, but it works. Unless I'm missing some menu somewhere, you can't make it save to an SD card - only built-in memory.
Also, you can't go through File Explorer and open the attachments, only through Pocket Outlook as described above.