You should set vim to not detach from the shell and be in the foreground. You can do this with the following command:
git config --global core.editor vim -f
From the man:
-f Foreground. For the GUI version, Vim will not fork and detach from the shell it
was started in. On the Amiga, Vim is not restarted to open a new window. This
option should be used when Vim is executed by a program that will wait for the
edit session to finish (e.g. mail). On the Amiga the ":sh" and ":!" commands
will not work.