isn't Aga Khan descended from Assassins ?
from the fate of other fanatical movement (Kharjites > Ibadi ), it seems natural that if survive, any movement including Assassins will mellowed out and become ordinary sect, at peace with its neighbour.
They had already did by the time of the Mongol invasion.
Also, rememeber they were not only a sect and a group of killers but also an organized political entity with fortresses, a small army, and a structured hierarchical leadership.
Much depends on how their relationships with the Khwarezmshahi or whoever is the top military power in Iran at the time evolve, politcally-wise. IOTL, the local Sunni rulers practically had begged the Mongols to rid them of the Ismailis, but there were times they allied with Sunni dynasties.
Yes, the Ismaili followers of the Aga Khans can be traced back to the Nizari Ismailism of the Assassins.