In fact, the NES colors are not real colors... it's just indexed colors (numbers). Every system interprets those indexed colors like they wants, NES, NES-clones, emulators...
You will never get the same result if you test on emulation, on a real nes, on a famicom, on a NTSC tv, on a PAL tv, ... always different results (sometimes between NES versions too).
It's also the reason why in the emulator's settings, you can choose which "palette" you want to use ... it means which rendered colors you prefer.
NES colors are just approximative colors.
You will never get the same colors than NESmaker. Sure, you could tell MESEN to use the same rendered palette than NESmaker, like explained here for example:
https://www.nesmakers.com/index.php?threads/nesmaker-palette-for-mesen.3432/
But it would be just for you, on your pc...
I suggest to play your game on a real hardware... because most people will play your game the way.