I have just been playing with this again for the umpteenth time.
The Home Story is simply the story it was first created on.
If you cut & paste onto another story, ArchiCAD will create an independent viewpoint that remains even when you paste the source marker back in. Why do we need that?!
One good way to control the visibility is to set the vertical range and have the marker just show partly or entirely within that range.
This is good when your story levels are set, but if you change them, all the markers need to be readjusted.
When we set the vertical range of a S/E/IE it should be linked to and update if we change our story heights.
I doubt anyone would want these to be static (relative to project zero) and not update if their building or story heights change.
Cheers,
Link.