I renamed the old /etc/bootmenu.d/backupmenu.item.
Then reinstalled the new 0.45 backupmenu, through untarring. No problem. Made a backup of both rootfs and optfs on the sd card. Noticed that the backup of the optfs was much smaller than the img (of course: the img includes the whole 2 gigabytes while the tar includes only the real files).

Then rebooted. When it woke up, it had a banner flashing once in a minute or the so saying the email client wasn't working, apmefo menu disappeared and the apps menu was lacking a great part of its icons.
So at least part of the /home partition was altered. Don't know if rootfs was in a trouble too.

Is it possible that the backup operation leaves the filesystem open and when shutting up it's left in an unconsistent state? But why on the optfs, while the tar file was written on the sd card?

I didn't go deeper in the issue because I needed the device, and went to restore a fortnight old backup made with your first method (img), which *is* reliable in my hands when flashing through another machine.

I don't know. Maybe it was a coincidence, and other peoples' reports can enlighten the issue. But... same thing happened when I tried your previous version, the one with tar, and two coincidences in a row are disturbing.