Ok I think I know what's wrong.
When I was in the app and saving the logs, I found the logs in my internal SD card (under /sdcard/RomCleaner) instead of the external SD card like how the app would lead me to believe.
Since OP said he doesn't have the S3, I can see why there's the mix up. For the S3, /extSDcard/ROMCleaner/ would normally mean the external SD card and not the internal SD card. The internal SD card is named as /sdcard.
I didn't try copying the user txt file over to the internal sdcard and flash because I'm using hypergalaxy and it's already super lean and doesn't have anything to remove, but if someone is using a more "normal" rom can try putting the ROMCleaner_user.txt file into the internal sd card and see if it works...