I have tried to give away multiple villagers, and they always disappear when I TT to the day they move D:
And then when I TT to the day before, they are not moving?!
You need to go to the day they tell you they are moving. For example, if they tell you they are moving on the 28th, they will be in boxes on that day and someone may claim them. If you go to the 29th, they will already be gone.
If a villager is moving on a certain day, Isabelle will tell you they is moving.
