HYDERABAD, India — When the Islamic State identified a promising young recruit willing to carry out an attack in one of India’s major tech hubs, the group made sure to arrange everything down to the bullets he needed to kill victims. For 17 months, terrorist operatives guided the recruit, a young engineer named Mohammed Ibrahim Yazdani, through every step of what they planned to be the Islamic State’s first strike on Indian soil. They vetted each new member of the cell as Mr. Yazdani recruited helpers. They taught him how to pledge allegiance to the terrorist group and securely send...