Yes, it's the same as the old G6 - the next time you turn on the DS, highlight the ROM you want and hit select to bring up a menu allowing you to choose which 'slot' to permanently back your save up into. If you continally play the same game, you don't need to back it up, since the save will simply stay in SRAM. However - if you don't back it up and play a different game, it will be overwritten.
Clumsy? Yes. You definitely need to think if you're playing multiple games.
Obviously you haven't tested it properly
That was the old G6 save system yes.. about 4 months ago since it got fixed though.
It does save to the default first save file from the sram directly everytime it saves. So you DON'T need to restart the nds just to backup the save file to savefile 2-3 etc cause it get's copied to the first save file and overwriting the sram save doesn't matter.
Just try it out.. play a few different games saving normally and then switch to another game without backuping, save there and back to the first game and you will see that the save is still there for both games.