Yes, when the game is moving someone in randomly, every time you turn the game off and turn it back on, the villager changes. But if you got someone from on here. Say like I got Tutu from someone on here, and I turned the game off then turned it back on, then it will always be Tutu trying to move in.
So if you turned the game off right now to plot reset Chevre, then it won't be Chevre moving in next time, it will be a different villager. Hope this makes sense.