Something that is a bit difficult to understand (and convey). This is a *full explanation*, so sorry if it's redundant with things you already understand:
For sprites, NES uses 4 "subpalettes" of 3 colors each + the transparent color which is the same in all. NESmaker uses the first two of these for game objects, and the second two of these for monsters.
When you are creating monsters, you are not actually setting their color, you are setting which subpalette they use (3 or 4), using the palettes that show there as reference for what those monsters will look like if put through those subpalettes. The SCREENS actually are what determine what palettes are placed in subpal 3 and 4. If you used the first choice of subpal when creating a monster, it will look like whatever you have placed on the SCREEN for that first monster subpal. And if you use the second choice, it will look like whatever you have placed on the SCREEN for that monster subpal. The palettes used when creating are just references, not actually tied to the monster itself necessarily.
Game Objects are similar, but where you set the game object palettes isn't on the screen, you set subpal 1 and 2 in the PLAYER game object. That determines which two subpalettes will be used for game objects (in sub pal slot 1 and 2). Whatever two subpalettes you set up in the player are the ones that all game objects will use. When creating, if you use the FIRST subpal to create (if it's selected when you're placing tiles in the animation) it will use whatever color set is in the first player sub palette. If you use the SECOND subpal to create, it will use whatever color set is in the second player sub palette.
I hope this makes sense!