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Please note that this is my interpretation of the note about a four-colors scheme, I am not the original author and so I may have misunderstood.

Here is a render from a Raumschach implementation for Table Top Simulator. It uses a four-colors scheme.

Opening the picture you can see that the two boards with a white corner have a different color scheme than the three boards with a black corner. The two boards are green, the three boards are brown.

With such colors when you move the Unicorn you have that if you go between green boards or between brown boards the square color will stay of the lightness level — start from a dark cell and arrive to a dark cell, or start from a light cell and arrive to a light cell. But if you go from a brown board to a green board or vice versa, then also the lightness of the cell will change, when the Unicorn starts from a dark cell arrives on a clear cell or when it starts from a light cell arrives to a dark one.

Disregard what I said the Jan 13, I finally played few games and I understood what the four color scheme is and why the sentence it is so confusing.

When reading "four-color scheme" one tends to think to four different colors like red, blue, green and yellow. But actually it is much better to think to two different hues and two different lightness levels.

Let use as example, red and blue, light and dark. You get four colors: light-red, light-blue, dark-red, and dark-blue.

With these four colors you can set up the chessboards so that the Bishop always stay in its starting lightness level, but may change hue. The Unicorn instead may change lightness color, but it will not change hue. A bishop starting on a light colored cell will play always on light cells, but it may change between red and blue. An Unicorn starting on a blue cell will play always on blue cells, but may change between light-blue and dark-blue.

How would it look like? The light-dark alternates as all Raumschach explanations you can find, the bottom-most, middle, and top-most floors have the dark cell in the corners, the other two floors have light cells in the corners. The red-blue instead would be the same in all five floors, the corner would be blue and the other cells have the hue alternated as you expect from a chessboard.

So, the bottom-most, middle, and top-most floors would have the corner square dark-blue, and the orthogonally nearby cells would be light-red. The other two floors would have the corners light-blue and the orthogonally nearby cells dark-red.