This is interesting, Alicia's ringers are actually mentioned in the series "Damsel in the Red Dress"
the ringer she has for Kattar sounds like a electronic rattlesnake sound, the one she has for Andrew is a maraca. these probably sound pretty similar so it's a wonder she knows who's calling her.
Kattar has a ringer for his friend Utkaresh that sounds like music from Megaman 8. His ringer for Alicia is a sample of the instrumental from "Still into You." by Paramore.
For "Hushabye Prince" characters:
Jinwoo's ringer is set to say the name of the people calling him. He finds a lot of ringtones grating, and they unsettle him.
Kimberly uses basic stock ringers, so her phone rings with the really boring default ringer heard in most skits for Hallie, and with "Over the Horizon" by Suga when Mad calls her.