You can just change the time to the middle of the day when they would be awake (12 PM for example) and check if they've moved out or not. But if you do this just be careful not to accidentally go to a new day or yesterday. Stay on the same day.
And if they haven't moved you can try trading them again
I don't think it's because of that! The same thing happened to me yesterday! Pinky was moving, and when someone adopted her, I had the "Pinky: Moved Out" sign. After I ran around the city for a while, I checked back on her again and she had the "Don't bother me, I'm sleeping" sign :/ it was weird! But she moved ok the next day and the person that adopted her got her, so... it might be a simple bug?