Why did Francisco Vásquez de Coronado have the man called "the Turk"
put to death?

im not exactly sure, but here hope this helps:

Francisco Vázquez de Coronado y Luján (1510 – 22 September 1554) was a Spanish conquistador and explorer who led a large expedition from Mexico to present-day Kansas through parts of the southwestern United States between 1540 and 1542. Vázquez de Coronado had hoped to reach the Cities of Cíbola, often referred to now as the mythical Seven Cities of Gold, which is a term not invented until American gold-rush days in the 1800s. His expedition marked the first European sightings of the Grand Canyon and the Colorado River, among other landmarks. His name is often Anglicized as "Vasquez de Coronado" or just "Coronado".