SANLIURFA, Turkey — When Abu Hamza, a former Syrian rebel, agreed to join the Islamic State, he did so assuming he would become a part of the group’s promised Islamist utopia, which has lured foreign jihadists from around the globe. Instead, he found himself being supervised by an Iraqi emir and receiving orders from shadowy Iraqis who moved in and out of the battlefield in Syria. When Abu Hamza disagreed with fellow commanders at an Islamic State meeting last year, he said, he was placed under arrest on the orders of a masked Iraqi man who had sat silently through...