There is one thing I don't get it : why does Jade turn into grimdark while being mind-controlled by HIC ? Wasn't that a specific thing from the horrorterrors ?

She doesn’t turn Grimdark, though! Okay, let me explain- The term ‘Grimdark’ is as it implies. Grim and Dark. It’s commonly used for bleak and sort of hopeless settings, dark settings. Rose turns Grimdark because of the Horrorterrors, getting corrupted to be more Voidy and do their bidding- And while Jade doesn’t get Horrorterror-corrupted, she still does become more Grim and Dark! She becomes an embodiment of everything negative and bad in Jade, and with her immense power, flipped against the Kids, things just look bleak. You may notice, she doesn’t speak in tongues, and her powers are still Space-related. She gave in to the Grimdark aesthetic, just not through Horrorterror Corruption.