After far too much effort, I believe I've figured out a workaround. The previous comment is correct, version 0.5.**.** doesn't support SD card offline playlists right now. I had to find a workaround, I knew they existed, but only version 0.4.12.180 worked for me. The stuff I found from Google worked after I used the aforementioned version without issue.
What I did to make it work:
1. Log out of the updated version of Spotify. (If it's not installed already, just don't install it at all. Much easier to start from step 3 if you can.)
2. Uninstall the old version.
3. Find and download version 0.4.12.180 of Spotify. For whatever reason, no other version allowed me to complete the next few steps with any success. I may just be incompetent, but I can only speak from my own experience. As with any download, find a trusted source. The file should be under 5 MB.
4. Install the old apk. Make sure you are able to install apps from unknown sources. ('Settings>Security>Unknown Sources' box checked means you can install it.)
5. DON'T LOG IN YET!!!!! At the login screen, hit the menu button and wipe the data.
6. STILL DON'T LOG IN YET!!! Now hit the menu button again and click SD card location. "/storage/extSdCard" is what I used (sans quotes, of course).
7. Now login with your credentials.
8. Download one playlist to your phone to create the directory in your SD card for Spotify.
9. Double check the "disk usage" information through the app or the desktop client and it should state the empty space on the SD card instead of the internal memory.
10. Update to the latest version and you'll still be saving music to the SD card instead of the internal memory.
11. Listen to your amazing music offiline from your SD Card.
Facebook
Twitter
Instagram