Tsunshun is slightly different than Tsundere. Instead of being a cold person (tsun) and later warming up to others (dere), Tsunshun characters are hostile to the people around them, then later feel sad and depressed, reflecting on their "tsun" actions when they are alone. The word "Shun...(しゅん。。。）" is derived from a Japanese sound effect representing melancholy, down, sad, depressed, etc.
The term "tsunshun" is coined by Nobara Yukinokouji who consider this to be a new form of moe.
Ririchiyo Shirakiin, the main character of Inu x Boku SS, is trying to fix this tsunshun attitude of hers. However it seems that the journey ahead is not going to be an easy one.
Ririchiyo is the first to display the tsunshun personality. At one moment, she insulted her friend with extremely mean words, but later wrote a long and proper apology letter to that same friend seeking forgiveness. A recurrence happened later, meaning that she refuses to properly reflect on her own mistakes, despite the fact that she promises not to repeat them.
Those who understand this personality or feeling would think of it as cute. Those who don't would misunderstood the character's well being entirely. This may require a proper study in the Tsunshun field: How to handle such persons with this attitude, and so on.
Either way, this archetype somehow does not create a negative impression on Ririchiyo's SS, Soushi Miketsukami.