If an Intro Story fadeout is interrupted by a loading zone, the game will load the map that is accessed by the loading zone and play a cutscene. Since every Intro Story scene starts with a certain cutscene number, the result depends on the time between pressing A to start Intro Story and triggering the fadeout.
- Fadeout 1 (0:55.0): cutscene 0
- Fadeout 2 (1:25.7): cutscene 0
- Fadeout 3 (2:36.5): cutscene 1
- Fadeout 4 (3:00.6): cutscene 7
- Fadeout 5 (3:25.1): cutscene 8
- Fadeout 6 (4:26.0): cutscene 0
The general idea is to trigger the Intro Story fadeout first and then have a loading zone interrupt it before the screen goes completely black. Do this after Intro Story reaches a specific part to get the corresponding cutscene.
For most maps, you need to die inside the loading zone by knocking yourself into it with oranges. To do this, you have to stand very close to the loading zone and bounce an orange off a wall or throw multiple oranges quickly to get hit by the explosion. Do not walk into the loading zone because if you get hit while there already is a screen transition, the Intro Story fadeout will cancel that transition and pull you into the intro cutscene. For the same reason, if you are extremely close to the loading zone, you may get knocked into it before the Intro Story fadeout starts.
There are some maps can be conveniently entered with a very short cutscene (less than the length of an Intro Story fadeout, which is about 1 second) that triggers an Intro Story fadeout, such as Creepy Castle and Chunky's minecart course.
There are also maps that can be entered with cutscenes that are longer than an Intro Story fadeout. You may need to do wrong cutscene on a different map in order to not get faded out out until the end of the cutscene. Generally, the time where you should activate the cutscene is [time of Intro Story fadeout] - [length of the cutscene] - 0.5s. For instance, if you want to skip the beetle race in Angry Aztec by triggering cutscene 1, you need to play your instrument at 2:36.5 - 23.2s - 0.5s = 2:12.8. There is always a +/-0.5 leeway since the Intro Story fadeout takes one second.
Most "wrong cutscenes" do not activate anything and merely make the camera go to where it normally goes during the cutscene.
Go here for a detailed analysis of wrong cutscene results.