I'm curious about the tiger's past life. Does the text give any backstory or karmic reason for why it came to Sai Baba?

Yes, Chapter 31 speculates on the tiger's past karma that led it to Sai Baba's feet for liberation. The text suggests that the creature might have been a meritorious person in a previous life who, out of pride in their learning, insulted a devotee of Hari. As a result of this offense, the person was cursed by the devotee to take on the 'cruel birth' of a tiger. However, the text also posits that a 'counter-curse' was in effect, which ultimately guided the tiger to Sai Baba. Through Sai's darshan, its sins were burned away, the bonds of past karma were broken, and it attained salvation, showcasing the wondrous and intricate ways destiny and grace operate.