axl: The same thing happens on my end, too. It unlocks the reversed/mirrored tracks alright, but doesn't record any time whatsoever. (Check under the Progress Table, there should be a green checkmark next to the completed tasks.)
tinyE: I googled it and found the answer.
You need to go into your Re-Volt folder and create a new folder called Times, then go into that folder and create four new folders called Mirror, Normal, Reverse, and ReverseMirror. That should do the trick. I should really look this stuff up before I waste everyone's time making a thread about it. :P
Actually, it wasn't a waste of time, because I just gave up on the times as not working. Since I could unlock the new layouts, I didn't care about them enough to Google such stuff. :P (But now I have a solution for that, thanks to you. Thank you!)
Meanwhile I updated my original post with a little more detailed info, maybe someone still needs it.