Just think about complementary colours and absorbtion. The blue-water filter transmits more yellow than the green-water filter. The exact absorbtion spectra are the secret of the filters' success, so you would need to do some research to identify them.
Tim
Left: Green water magic filter
Right:Blue water magic filter
I know that magic filters combine recipe of color temperature conversion and color compensation.
BUT I don't know why the bule water filter must be orange while the green water one must be red.
Any scientific explanation in depth?
Since you ask for a scientific explanation you may be interested in an old post of mine measuring and simulating colour absorption spectra for the blue water filter and "idealized" seawater. Depending on the types of particulates and algae the filter needs to have a different absorption spectrum leading to distinct blue water and green water filters. With the new high ISO capabilities and better AF at low light filters should be even more attractive. You can find the old post here