Unlike the past iterations, ACNL does cause a villager to move out when TTing backwards. Even if we think that going back to the past shouldn't harm them. Why the developers did that is actually a mystery.
Moving out villagers is easy when you do the day by day forward method. Just make sure you talk to all if not most of your villagers to see who's thinking about moving or who pings you. It's always been easy for me because I almost always have 9 villagers. One moves out, one eventually moves in, four days later someone wants to move out.
Going backwards counts as one day in villager moving cycles. If someone is already moving, it counts as a day towards it and if you didn't know when they were supposed to leave you can easily find them packed or even gone if you weren't paying attention. But if you know no-one is moving (or when the next move is occuring) you will be fine. I've tracked this several times while moving out villagers for my friends -- it has never been a problem. In your case, you just want to get rid of the villager? So the day they are in boxes, immediately jump backwards. They will have moved but no-one else can move out.