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It is all about triangles.
At opposition Jupiter-Earth-Sun angle is zero in one plane and a few degrees in another. Either side of opposition the Earth-Jupiter-Sun angle increases to a maximum determined by the size of the orbits and then shrinks back to zero at conjunction (Earth-Sun-Jupiter).
Draw a triangle with Earth, Jupiter and Sun at each apex. Then draw small circles around Jupiter representing the satellite orbits.
Just look at a single plane for the time being for simplicity. When a satellite is in line with Earth-Satellite-Jupiter the disk is seen to cross planet's surface for observers on Earth. When a satellite is in line with Sun-Satellite-Jupiter the satellite disk would be seen to cross the planet's surface from the Sun but its shadow would be seen to cross the surface from the Earth.
The geometry is a little more complex due to the inclined planes of Earth, Jupiter and all the satellites. Have a look at Jupiter2 software and look at the Polar view (bottom left). The Sun is represented as a yellow dot at the bottom of the picture and the direction toward Earth is the small vertical line. Note the other side of opposition would have the Sun on the left. (When Jupiter is in the pre dawn sky in the east).
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