The 20-year-old singer sees her role on the judging panel as a huge "privilege" because she is paid to "mess with" the show boss.
She said: "It's pretty amazing that I get the privilege to get paid to mess with my boss all day.
"Behind the cameras, when we're not on the panel, we do get along really well. He says the sign of being able to tease each other is a sign of comfortability (sic) - and I say, 'Yeah it's just a sign of me still hating you.' "
Demi also joked that she initially told Simon she was "too busy" to take a role on the show alongside him, L.A. Reid and Britney Spears.
She told TV talk show host Jimmy Kimmel: "I didn't have an interview, I'd never really met him. I had met him on 'American Idol' a couple of times but he didn't remember me... don't worry about that, he knows me now. He knows what he's doing, he's really smart and I hate him.
"He just called up one day and I was like 'I dunno, I'm too busy for your little show. Britney who?' and then he begged me so I said OK."
Viewers recently saw Demi take the seat on the panel next to Simon, which had previously been held by Britney, and the 'Skyscraper' singer admits producers requested she move because of her rows with the music mogul.
She explained: "We were just playing musical chairs. We were sat that way and I guess they hated me bending over to yell at Simon the whole time so they put me next to him, what a great idea."