I'm not sure of this, but I think if you keep near the center of the area (where the man was murdered), the cutscene will be triggered a lot faster. There is no other part in the game that happens something similar (weird) like that.
The game doesn't sucks, but it's not that great either.
Edit: The Gamecube version is not that great because of the controls. The Wii version is a lot better.
Castlevania Judgment FC: 1161 - 3389 - 1512
3DS Friend Code: 3480-2746-6289
Wii Friend Code: 4268-9719-1932-3069