I'll try to answer your question, sorry if it doesn't satisfy you

So basically after the fall of Alamut and the overall downfall of the Nizari state, the Nizari Isma'ili was divided into two branches, the Qasim-Shahi and Muhammad-Shahi because there's a succession dispute in the family. Details are blurry and there's not much known about the dispute, but there are three versions of it. First is coming from oral traditions of the Syrian Muhammad-Shahi Nizaris. The death of the 25th imam Shams al-Din Muhammad was disputed by his eldest and youngest son, Ala'al-din Mu'min Shah and Qasim Shah. According to Syrian tradition, Qasim Shah was merely acting as the hujja (regent, essentially) for Mu'min Shah who will in due course be succeeded by his son Muhammad Shah. Second is from a 17th century Muhammad-Shahi Nizari literature Lama'at al-Tahirin. In this version, Mu'min Shah, succeeding Shams al-Din was the father of Qasim Shah and Muhammad Shah and on their father's death, both claimed his succession. Third is from the Qasim-Shahi traditions, where it stated that Mu'min Shah named Mu'min Shah as his successor, and after that Mu'min Shah was succeeded by his son Qasim Shah. Whatever the truth is, the dispute split the Nizaris in two. Muhammad-Shahi Nizari enjoyed a popularity in Central Asia and Syria, while the Qasim-Shahis enjoyed popularity in India and Persia.

The Muhammad-Shahi lines of imam would eventually died out (There are still a number of Muhammad-Shahi Nizari adherence living today in Syria) but the Qasim-Shahi imams survived and would obtain the title of Agha Khan. The Qasim-Shahis, while able to live out their lives in Persia was sometimes persecuted depending on the ruler. In 1817, the 45th imam Shah Khalil Allah III was killed after a dispute between the Nizari and Twelver followers. He was succeeded by his thirteen year old son Hasan Ali Shah as the 46th imam. After a dispute in Mahallat left the family penniless, Hasan Ali's mother went to the Qajar court to seek justice for her family. Her pleadings was heard, mainly because the Qajari shah and Shah Khalil Allah was close friends. The instigators of Shah Khalil's murder were punished, returned the family's properties, and gave one of the shah's daughter in marriage to the imam. Not only that he also appointed the imam as the governor of Qom and bestowed on him the laqab (title) of Agha Khan, meaning lord and master. Henceforth, Hasan Ali Shah was known as Agha Khan Mahallati because of his royal titles and family's deep roots in Mahallati area. The title of Agha Khan remained hereditary amongst his successors, the Nizari Qasim-Shahi imams of modern times

Sources

The Ismailis, Their History and Doctrine by Farhad Daftary. This is pretty much the best book on the Ismailis available in English, and if you want to know more you should check it out