He usually wears this mask in the retelling to hide his identity, or kidnap a Chiranjeevi (he wore this when he kidnapped Vibhishan) or someone from Kalki's friend circle. If you find him in a crime site, you'll see this version.
The sweet pastelcore Kali (who's fake name is Kairabh) is Just Some Guy™ that people know. He actually used to be a close friend of Kalki (whose birth name is Amar) before he knew he was Kalki, after which he started distancing himself as he started scheming more. He doesn't hate Kalki because he's a God. He hates him because of the prophecy. That this guy will be his doom. The light to his darkness.
So pastelcore Kali is only around Kalki and his friends. When he needs to show his dark side, he sports this mask.
Eventually when he reveals his true self he shows the caricatured portrayal of Asurs through the mask. How they're always portrayed as outlandishly monstrous, when they might as well look... Just like the Devas, hence using this tactic to contrast how the Devas are portrayed and to manipulate Vibhishan (since he's also an Asur) thereafter to get him to his side.