The game's native story progression setting needs only rechecking if your game folder is new. It is ticked (enabled) by default. LaPaige, I also suggest double checking your setting.
When you hover your mouse (not visible in the picture) over the story progression option, this explanation pops up. If story progression is disabled, townie Sims do not move into empty houses. Nothing I have ever played with in terms of mods and CC, save for the NRaas Story Progression mod, has ever interfered with the game's native story progression setting.