Thanks for a bug report. Does evolution claim anything during the restore? You can see its console output (where most of the messages end) when you run evolution form a console. There had been done some fixes in restore for 3.8.1, which was released just yesterday, and it'll be available in updates-testing within this week.

IN this chase there has been restere off new file into evolution.
From File > restore backup ( selected old file )


$ evolution 
** Message: First result 0
evolution.dir
** Message: Second result 0
evolution-backup-restore-Message: Sanity check result 1:0 0
** Message: First result 0
evolution.dir
** Message: Second result 0
** Message: evolution --quit
** Message: mv /home/floki/.local/share/evolution /home/floki/.local/share/evolution_old
** Message: mv /home/floki/.config/evolution /home/floki/.config/evolution_old
** Message: cd /tmp && tar xzf '/mnt/ymislegt/geyma/evolution-backup-20110901.tar.gz' evolution.dir
** Message: cd /home/floki/.local/share/evolution && tar xzf '/mnt/ymislegt/geyma/evolution-backup-20110901.tar.gz' '.local/share/evolution' --strip-components=3
** Message: cd /home/floki/.config/evolution && tar xzf '/mnt/ymislegt/geyma/evolution-backup-20110901.tar.gz' '.config/evolution' --strip-components=2
** Message: gconftool-2 --load /home/floki/.local/share/evolution/backup-restore-gconf.xml
** Message: gsettings-data-convert
** Message: rm /home/floki/.local/share/evolution/backup-restore-gconf.xml
** Message: rm -rf /home/floki/.local/share/evolution_old
** Message: rm -rf /home/floki/.config/evolution_old
** Message: rm /home/floki/.local/share/evolution/.running
rm: cannot remove ‘/home/floki/.local/share/evolution/.running’: No such file or directory
** Message: gdbus call --session --dest org.gnome.evolution.dataserver.Sources1 --object-path /org/gnome/evolution/dataserver/SourceManager --method org.gnome.evolution.dataserver.SourceManager.Reload
()
[floki@localhost ~]$ 
(evolution:5156): Gtk-CRITICAL **: gtk_entry_set_text: assertion `text != NULL' failed

(evolution:5156): Gtk-CRITICAL **: gtk_entry_set_text: assertion `text != NULL' failed

(evolution:5156): Gtk-CRITICAL **: gtk_entry_set_text: assertion `text != NULL' failed

(evolution:5156): Gtk-CRITICAL **: gtk_entry_set_text: assertion `text != NULL' failed

(evolution:5156): Gtk-CRITICAL **: gtk_entry_set_text: assertion `text != NULL' failed

(evolution:5156): Gtk-CRITICAL **: gtk_entry_set_text: assertion `text != NULL' failed

(evolution:5156): Gtk-CRITICAL **: gtk_entry_set_text: assertion `text != NULL' failed

(evolution:5156): Gtk-CRITICAL **: gtk_entry_set_text: assertion `text != NULL' failed


------------
Evolution Account Assistant Window pops up.

there select old file 

---
** Message: First result 0
evolution.dir
** Message: Second result 0
evolution-backup-restore-Message: Sanity check result 1:0 0
** Message: First result 0
evolution.dir
** Message: Second result 0
** Message: evolution --quit
** Message: mv /home/floki/.local/share/evolution /home/floki/.local/share/evolution_old
** Message: mv /home/floki/.config/evolution /home/floki/.config/evolution_old
** Message: cd /tmp && tar xzf '/mnt/ymislegt/geyma/evolution-backup-20130409.tar.gz' evolution.dir
** Message: cd /home/floki/.local/share/evolution && tar xzf '/mnt/ymislegt/geyma/evolution-backup-20130409.tar.gz' '.local/share/evolution' --strip-components=3
** Message: cd /home/floki/.config/evolution && tar xzf '/mnt/ymislegt/geyma/evolution-backup-20130409.tar.gz' '.config/evolution' --strip-components=2
** Message: cat /home/floki/.local/share/evolution/backup-restore-dconf-eds.ini | dconf load /org/gnome/evolution-data-server/
** Message: rm /home/floki/.local/share/evolution/backup-restore-dconf-eds.ini
** Message: cat /home/floki/.local/share/evolution/backup-restore-dconf-evo.ini | dconf load /org/gnome/evolution/
** Message: rm /home/floki/.local/share/evolution/backup-restore-dconf-evo.ini
** Message: rm -rf /home/floki/.local/share/evolution_old
** Message: rm -rf /home/floki/.config/evolution_old
** Message: rm /home/floki/.local/share/evolution/.running
rm: cannot remove ‘/home/floki/.local/share/evolution/.running’: No such file or directory
** Message: gdbus call --session --dest org.gnome.evolution.dataserver.Sources1 --object-path /org/gnome/evolution/dataserver/SourceManager --method org.gnome.evolution.dataserver.SourceManager.Reload
()
----
wakes upp in innbox

Thanks for the update. I see the old backup (20110901) still uses the gconf data, while the new backup (20130409) uses dconf. The old backup doesn't restore GConf account setup properly, or, more precisely, the gconf daemon doesn't save data to disk in a quickly enough. Could you try this (as a workaround), please:
a) restore from the old backup
b) when the wizard opens again, close it
c) extract 'backup-restore-gconf.xml' from the old backup
d) run these two commands on it:
   $ gconftool-2 --load backup-restore-gconf.xml
   $ gsettings-data-convert
e) wait for couple seconds (10-30), specifically till
   ~/.gconf/apps/evolution/mail/%gconf.xml
   is not updated with your accounts. You can query the gconf like this:
   $ gconftool-2 --get /apps/evolution/mail/accounts
   which should return some long list (all your mail accounts), not only [],
   but it's no guarantee that the data are saved on the disk (the source registry
   process reads data from disk, not through GConf)
f) once the data are on the disk, invoke the source registry reload:
   gdbus call --session --dest org.gnome.evolution.dataserver.Sources1 --object-path /org/gnome/evolution/dataserver/SourceManager --method org.gnome.evolution.dataserver.SourceManager.Reload

At this point the
   $ gconftool-2 --get /apps/evolution/mail/accounts
should only return [] and ~/.config/evolution/sources should contain .source files with migrated accounts.

Let's deal with this within bug #981712, which has more details.

*** This bug has been marked as a duplicate of bug 981712 ***