Some Sith (the Dark Siders) such as Anakin Skywalker and Palpatine have yellow eyes. This eye color comes with a deep embracing of the Dark Side and the level of corruption. The immersion gives one more power to do things and get involved in different atrocities. They become corrupt, get willpower, and become destructive which changes them physically. It is this power that transforms their bodies and eyes which becomes a sign in their world. Yellow eyes signify a loss of control. The Sith is controlled by dark forces.
Maul who was raised by Palpatine is fully immersed in the Dark Side. It is through this that he became an apprentice of Palpatine and it explains why his eyes are continuously yellow. While he died in Kenobi’s arms, his eyes never went back to normal. A Magick was cast on Savage Opress and this is when his eyes turned to yellow. Whenever he was enraged, his eyes could turn color. It is only after the Magick was withdrawn that they turned into natural green-blue color.
There is a reason why the sith develops yellow eyes, but it all boils down to their level of corruption in the Dark Side. You will notice that some sith such as Count Dooku and Yoda does not have the yellow eyes. They fail to get them as they have not fully embraced the dark side which means they enjoy self-control. We are going to go deep into why they develop these eyes.