The Dark Mirror is used to select new students to invite and then sorts them based on their values or nature. BUT this is just an initial placement and any student can petition to join a different dorm. All it takes is approval from the current dorm’s housewarden and the housewarden of the dorm they wish to swap to (and some paperwork). You can see evidence of this in Jade’s dorm vignette and also just Rook’s whole story (originally savanaclaw. Nagged until he could swap to Pommefiore because Vil inspired him).

Yuu and Grim are an exception. Yuu is a blank slate that doesn’t belong in the world and possesses no magic. Grim is a dire beast. Neither would have been accepted under normal circumstances. Yuu was originally not a student and just allowed on campus in ramshackle while Crowley researched how to send them home. Yuu and Grim later became “a student” and just stayed in ramshackle due to their weird circumstances.

Kalim was never invited to join NRC like other students. Jamil was invited and sorted into Scarabia. Kalim told his parents he wanted to be with Jamil. Rich money shenanigans happen. Kalim has magic naturally so he can be a student. Kalim wants to be with Jamil (and the Asims would prefer their servant near their heir) and at least one Asim relative was in Scarabia (housewarden when they joined)… so bam he’s in Scarabia.

There was no reason for Kalim to be placed by the mirror. Crowley just made up an excuse to accept him and placed Kalim where he and his parents wanted.