Motor Daddy:
Here is a picture of what happens in reality (i.e. the world described by Einstein) for your source in a square box:
The three diagrams on the left-hand side show successive snapshots in a reference frame in which the box moves to the right with some speed. The three diagrams on the right show the same snapshots in a reference frame in which the box is stationary.
Or, to put it another way, the left-hand diagrams show the situation in the frame of the "embankment", where the box is on a moving train. The left-hand diagrams show the same situation in the frame of the "train".
The first thing to notice is that the box is square on the right and rectangular on the left. This is due to length contraction. In the train's frame, the box is at rest so it is square/cubical. In the embankment frame, the box is moving and so relativity tells us that it contracts in the direction of motion.
Also note that in the left-hand diagrams the box moves to the right, because the embankment sees the train moving to the right. In the right-hand diagrams, the box does not move, because a person on the train does not see the box move.
The next thing to notice is the round dot marked on each diagram. That is the location at which light was emitted, which doesn't change in each frame.
Next thing: the three diagrams show the light wave spreading out. The wavefront is
circular/spherical in BOTH frames, due to Einstein's speed-of-light postulate. Note in particular that in the Motor-Daddy universe the wavefront would NOT be circular in the train frame, since the speed of light travels at different speeds in different directions in the Motor Daddy universe.
The top two diagrams shows the wavefront a short time after emission.
The middle diagram on the left shows the wave hitting the "back" wall of the box in the embankment frame.
The two bottom diagrams shows the situation when the wave hits the "front" wall of the box. Notice that in the train frame the wave also hits the back wall at this time.
The middle diagram on the right shows a time in the train frame where the light wave has not yet reached either wall of the box.
Next thing to note: in the train frame, the light wave hit both the front and back of the train simultaneously (as shown in the bottom-right diagram). In the embankment frame, the walls were hit at two different times - first the back wall (middle-left diagram), then the front wall (bottom-left diagram).
It is important to remember that two different clocks are being used on the right and on the left. The diagrams on the left use the embankment clocks; the diagrams on the right use clocks on the train.
