Each of these stories culminates in a murder (the novel The White Tiger and the movie Theeb). How justified was each murder, respectively, and how does this murder and its justification serve as an embodiment of the core theme of each story?

Let's first consider the plot of each of these stories:
The movie Theeb, written and directed by Naji Abu Nowar, follows the story of the titular Theeb--an orphan who is the third son of a Bedouin sheik--as he attempts to survive in the Wadi Rum desert in 1916. In the film, Theeb and his older brother, Hussein, help guide a British officer, Edward, and an Arab man, Marji, to a Roman well that borders the Ottoman railway. However, shortly after discovering that the well is contaminated with dead bodies, Edward and Marji are shot by a gang of raiders. Although Hussein and Theeb manage to make an initial escape, Hussein is soon thereafter murdered by one of the men, and Theeb falls into a well. Theeb manages to climb out and eventually stumbles upon an unconscious man stationed on a camel. This man is Hassan, an injured mercenary. In their equally weakened states, Hassan and Theeb assist each other in escaping the desert terrain. They manage to make their way to an Ottoman railway station, discovering in the process many dead Arab revolutionaries who had depended on Edward's survival (as we learn that he was in possession of a detonator which was meant to blow up the railway). Hassan winds up selling Edward's belongings, which triggers a realization in Theeb: Hassan has betrayed his Arab brethren in supports of the Turks. Thus, Theeb shoots Hassan, killing him as revenge for this deceit and for the death of Hussein. 
Aravind Adiga's novel The White Tiger follows the story of Balram Halwai, the son of a rickshaw puller, who explains his escape from servitude through letters to the Chinese Premier, Wen Jiabao. Balram leaves behind his village of Laxmangarh to work in a teashop in Dhanbad, where he learns how to drive and gains knowledge about India's government by eavesdropping on his customers. He begins working as a driver for Ashok (a son of the city's landlord) and abandons his affiliations with his family, eventually making the move with Ashok and Pinky Madam (Ashok's wife) to New Delhi. After Pinky Madam runs over and kills a child while drunkenly driving Balram's vehicle one night, Balram is pressured to take responsibility for the death. Balram instead decides to murder Ashok in order to escape the "Rooster Coop." This sets off a chain of other violence, with Balram later paying off the family of a bike messenger killed by one of Balram's new business's drivers and with Balrom certain that his family has been murdered by Ashok's relatives as revenge. 
Your question of how "justified" each respective murder was is a difficult one. I don't know that we can necessarily say murder is ever justified--whether fictional or not--but perhaps we can consider the motives and emotions that supported these characters' actions.
I would argue that Theeb's decision to murder Hassan is a much more sympathetic (and, thus, "justified") one than Balram's decision to murder Ashok. Theeb is just a child who has been rendered totally alone in the world by the death of his brother; the murder is arguably an act of passion and awakening as Theeb transitions from adolescence into adulthood. This murder of Hassan was one that also represented an important political agenda/theme--the tensions in the Middle East during World War One and the Great Arab Revolt against the Ottoman Empire.  
Balram, on the other hand, had much more agency in his situation, and his decision to murder Ashok is one motivated out of self-interest rather than as revenge for some injustice. Balram's egotistical obsession with his own "freedom" at the cost of the lives of others is problematic. While his individualistic spirit and personal quest for autonomy may be inspiring thematically as he rises out of the "darkness" of the lower caste, it is ultimately achieved at a high price. One could understand why he did what he did, but it is also a more difficult decision for readers to swallow.