If you copied the files to the new partition but didn't delete them from the root partition, the old ones are masked or hidden by mounting the new partition on top of them. In that case, you should still have the same amount of root partition being in use, no space being freed. Unless we both missed that part, deleting the old copies is not included in the instructions you linked.
I'm quoting here a good answer on the subject:
When you mount a filesystem on a directory
/mount-point, you can no
longer access files under
/mount-point directly. They still exist, but
/mount-point now refers to the root of the mounted filesystem, not to
the directory that served as a mount point, so the contents of this
directory cannot be accessed, at least in this way.
The most straight-forward way to straighten this out is, of course, by
umounting the new
/home (in order this to succeed, no files from
/home must be in use, meaning only root can be logged in), then you'll see the old files (which occupy root partition) and can delete them to free space in the root partition (but do double-check that the new partition is not mounted before really deleting anything). You should probably delete everything under the old
/home, not just the contents within the user directories.