I was taking a walk yesterday, and I was listening to music in my personal library. No Apple Music subscription. After awhile, my music stopped. I checked, and it said something about needing internet to access music and turning on cellular music in settings or something like that. It happened again today at the mall. I'm confused… I thought that my personal library was on my device. Is it? By the way, I am using an iPod touch 6th generation and running (gulp) iOS 9 public beta. My best guess is it's the beta. Maybe they don't want all my music on my device in case I have to reset it. But wouldn't it be backed up to iTunes?
Need internet to listen to the music library
ipod-touchitunes
Related Solutions
The only means I have ever found of doing this is third-party software. I have used Senuti for this, and can confirm that it works.
The current version of Senuti: http://www.fadingred.com/senuti/. The free trial version allows you to restore up to 1000 songs. There is also a fully-free version from 2008 [MD5 (Senuti.0.52.dmg) = e84ebf4614ded95c53dc750492297c87] at http://wstein.org/senuti/, but though the source code is available (there and at SourceForge), it has not been maintained, and I have not confirmed that it still works. (You can get an older version from the developer, too.)
There is also TouchCopy: http://www.wideanglesoftware.com/touchcopy. It appears to be very complete but is expensive, and the trial version is more limiting than is that of Senuti.
They are referring to the "Purchased" under the "Quick Links" section on the right of the iTunes Store Home Page. Once you do this "Songs of Innocence" will be added to your "Purchased" playlist on the left.
Best Answer
Yipee! I figured it out! My problem is, as I forgot to mention in the question, I just got a new iPod. Aaaaaaand, I never realized it, but apparently when you get a new device, you have to download all your music into your library. Otherwise, you can still listen to it, but only over internet. Probably to save space. Downloading your songs can be done by tapping on the song or album, and then tapping "Make available offline".
Thank you everyone for your help!