I'll give a little context before I ask the questions, though I will put a TLDR at the bottom. Recently I have been playing Panel de Pon on the Nintendo Puzzle Collection for the Gamecube. The gameplay itself is Tetris Attack/Pokemon Puzzle League, which are both reskins and updates of the original SNES version of the game. With that out of the way, I'll explain my questions are on a TAS site and not some site related to the game itself.
I decided to play the game in slow motion (where the tool assisted aspects start to come in) to help practice for lack of a better term, but quickly found myself recording inputs, using savestates, among other things to have some fun. Everything seemed to work as intended only there was one issue, whenever I tried to playback multiplayer recordings, the blocks used for it were different each time (thus the recorded inputs would not be working correctly). This did not happen with single-player recordings.
I am going to assume the block patterns are generated through the RNG, and I am also going to assume the RNG is either different, or uses different functions, for multiplayer, and somehow player inputs are not effecting the RNG in the latter (otherwise it would of been the same). I understand this is a specific game and this wouldn't be the place to ask about game specifics, but my questions are more general.
Is this a common thing? That being games that have RNGs that are not effected by any sort of input the player does, nor any sort of clock tied to it (I understand for some, game time effects it instead). Also is there any sort of methods to help figure it out? Or is it merely trial and error and hoping for the best?
TLDR: Are RNGs that don't appear to be effected by any player inputs common? And is there any sort of method to learning how they function faster? Or is it merely trial and error?