I explain how spawning displacement works. This is a glitch only present on the Japanese version of the game. The glitch stems from the fact that a moving platform's movement will apply to Mario for one frame too many when he leaves an area. More specifically, if Mario dies, collects a star, or exits out on a moving platform, then that platform's movement will apply to Mario for one frame after he appears in the castle (or anywhere else).

Note that the platform's movement applies to Mario's new position (i.e. where he spawns), and not his old position (i.e. where he dies/collects a star/exits out). Thus, in order to understand the effect of the platform's movement on Mario, it's necessary to examine where the platform is in relation to the coordinate system of the new area. Then, apply one frame's worth of movement to Mario's new position to determine the spawning displacement. For rotating platforms, this one frame of movement can result in displacements much larger than the displacements you would normally get while on top of the platform. That's because the effect of a rotation is magnified the further away from the axis of rotation you are. Thus, one can achieve greater spawning displacements by using a rotating platform that's both rotating fast and far away from the spawning position. Translating platforms can also yield spawning displacement, but the displacements aren't nearly as large as the ones from rotating platforms.

Note that not all moving platforms allow for spawning displacement. Specifically, only platforms that have traction allow for spawning displacement. That means that as the platform translates/rotates, it moves Mario with it. If Mario is standing on a platform and it's able to move out from under him, then that platform doesn't have traction. Additionally, since spawning displacement takes place between two areas, all the objects in the first area must unload and then all the objects in the second area must load. If this unloading/loading causes the moving platform to be overwritten by a new object, then spawning displacement won't occur. However, if the new object is itself a moving platform, then reverse spawning displacement will occur, which doesn't' depend on the movement of the first platform.

Additional Notes
(1) I had said that the hand in TTC only has 2 possible spawning displacements, but that wasn't exactly true. When the clock hand ticks, it moves 1092 angle units over a 6 frame period. You see, it can only move a maximum of 200 angle units per frame, and so it moves 200 angle units for 5 frames and then 92 angle units on the 6th frame. So that means that depending on whether you leave the level on one of the first 5 frames or on the 6th frame, the magnitude of the angular velocity will be different. And so since there are actually 2 possible angular speeds and 2 possible directions, that makes 4 possible velocities, and so there would be 4 spawning displacements.
(2) I realize that my example wasn't very good for when I showed that the pit block being overwritten by the TTC painting minute hand didn't yield any displacement. That's because if it did yield displacement, it wouldn't be observable anyway, since Mario exits the painting exactly on the axis of rotation for the minute hand. Nevertheless, I've tested that concept in other ways as well (e.g. using the the TTC painting pendulum and also a star marker), so I know it to be true independent of the results of that one example.
(3) One of the perks of using the WDW rotating platform was that I could actually control what object slot it was in. Specifically, I had gone through the loading point back and forth several times until the rotating platform was in a sufficiently high slot. The reason for this is that when transitioning between areas, it's the lowest slots that get occupied by the new objects. So the only platforms that are suitable for spawning displacement are ones located in objects slots high enough to avoid having objects in the new area will load into their slots. Having your moving platform be overwritten when spawning in the castle isn't all that frequent, since the castle has relatively few objects compared to the main levels (so most objects from the level aren't overwritten). However, this issue is quite common when spawning in another one of the main levels when trying to desync the demos, and so using a platform that's in a high slot is critical for that. Unfortunately, for most objects, we have very little to no control over what slot they occupy. But courses with loading points are the exception.
(4) This glitch has been known for a very long time, and it has already been incorporated into an A Press save strat shown here:    • SM64  Stop Time for Red Coins & Reen...  . This can only be done with the red coin star, because it's the only cloneable star in the course (besides the 100 coin star).