If you did have RFC Dawn of Civilization installed before you downloaded this mod, you need to rename the mod folder to something else. (This is because you can't have 2 folders with the same name) Then, leave that folder alone. (This is the "creating a backup" part)
Then, unpack the AllCivs mod in the BTS/Mods folder. Rename the folder of the Allcivs mod to "RFC Dawn of Civilization". Now you can play the mod as normal.
Do NOT copy the Allcivs mod into the "backuped" folder. That will not work. (And it could possibly corrupt that mod because some files get conflicted)