5. Retrospection
@sourcejedi has provided a useful answer below.
What happened is that the content of the directory storage/ was always saved in sda8 as /home/user2/storage, whether user1 or user2 were logged in, and mounted on sda13 when user2 logged in. Say storage/ contained 100G, then 100G were always taken on /dev/sda8 and some times in /dev/sda13.
I discovered this by mounting /dev/sda13 on a brand-new /home/storage from the /etc/fstab file: I was logged in as user2 and all files were still in /home/user2/storage within /dev/sda8. So I moved the files to a directory within the partition sda13, and referenced such a directory with a symlink from inside /home/user2, as suggested.
In this way I freed those 100G in sda8 and have a reliable report of the size of storage/ from df -h /dev/sda13 whether I am user1 or user2.