That's what their website says, however I had a play and created a file and logged in and out and the file persisted as did my ability to look at the /onion directory via Tor after the ssh session was stopped.
It does shutdown when you log out, the only persisted data in on /sec and /everyone
Your home directory is in /sec/root.
If you install tools outside of /sec/usr they will be reset on your next visit. So if you want to install something that survives a session log out you need to install to /sec/usr
I read somewhere on their site or in GitHub that files in the home directory are encrypted when you disconnect and when you connect again the encrypted file is restored and so you have files back. If you were to install a program with apt however when you log in again that will be gone.
Your home directory is in /sec/root.
If you install tools outside of /sec/usr they will be reset on your next visit. So if you want to install something that survives a session log out you need to install to /sec/usr