I created a docker container, and then I created a file and exited the container.
When I restart the container with:
docker run -i -t ubuntu /bin/bash
the file is nowhere to be found. I checked /var/lib/docker/ and there is another folder created which has my file in it. I know it's something to do with Union FS.
I don't know if this will answer your question completely, but...
Doing docker run -i -t ubuntu /bin/bash will not restart any container. Instead, it will create and start a new container based on the ubuntu image.
If you started a container and stopped it you can use docker start ${CONTAINER_ID}. If you did not stop it yet you can use restart.
You can also commit (export) the container to a new image: see http://docs.docker.io/en/latest/commandline/command/commit/ for the correct syntax. docker export is a option as well, but all that will do is archive your container. By creating a new image using docker commit you can create multiple instances (containers) of it afterwards, all having your file in it.
docker attachUnion FS did not have anything to do with your question (with you new info) please update the question, and if you actually use the posted answer, select it so people know what actually answered your question.