He is a member of Salem's group.
Tyrian is very loyal toward Salem, even referring to her in "Tipping Point" as a goddess to whom he belongs.
After becoming too wounded to win the fight against Qrow and Team RNJR, he tells himself that she will forgive him before retreating. This indicates that he is afraid of Salem.
In "Taking Control", his extreme loyalty to Salem manifests itself dramatically. When he realizes that he has disappointed her, Tyrian suffers a mental breakdown, crying in despair and taking out his pain out on a Beowolf that he delivers a sadistic beating to.
Despite his psychotic demeanor and overall lack of regard for most forms of life in general, Salem's approval is the be-all and end-all for Tyrian. To him, she truly is the divine, and her will and approval is little short of doctrine in his deranged mind.
Tyrian holds Cinder in low regard. He mocks her repeatedly after the loss of her left eye, and when Ruby believes that Cinder is the "goddess" that Tyrian refers to, he scoffs at the notion that she is worthy of such a title. He is also comfortable enough in her presence to show his grief and mania when he disappoints Salem. However, Cinder shows clear discomfort and horror watching his reaction.
Tyrian is very eager to hunt her down as he is planning to take one of her eyes in retaliation for Cinder's similar injury, though given Tyrian's interactions with Cinder, this appears to simply be his justification for wanting to bring down the young Huntress to sate his general blood lust and to raise his standing in Salem's eyes.
During his fight with Team RNJR, he declares his purpose to take Ruby with him. After depleting her Aura, he attempts to deliver a severe blow on her with his scorpion tail.
After the fight with Team RNJR and Qrow, Tyrian calls Ruby a bitch for cutting off his stinger.
Tyrian expresses an interest in Jaune for unknown reasons in "Tipping Point".
When Tyrian is about to sting Ruby, Qrow steps in and blocks his attack. Tyrian reveals that he knows Qrow and calls him a true Huntsman. The two of them fight, and it is shown that they are equally matched. When Ruby intervenes, Tyrian manages to graze Qrow with his stinger.