Who were the people over whom Montezuma of the Aztecs ruled?

You’ve actually answered your own question:  Montezuma ruled over the Aztec Empire.  There were actually two Montezumas; during the reign of the first, the Empire’s Triple Alliance was solidified.  This was a unification of Montezuma’s own Tenochtitlan, the chief city of the Aztecs, with the neighboring powers of Texcoco and Tlacopan.  Montezuma I ruled over both these peoples.  He also conquered a vast expanse of land in present-day southern Mexico, until the Aztec Empire reached from the Pacific Ocean all the way to the Gulf of Mexico.  In this process, Montezuma took over the lands of the Huastecs and Totonacs, the Mixtecs, and the cities of Orizaba, Cotaxtla, and Cosamaloapan.

Montezuma II was emperor in the sixteenth century, when the peoples of Mesoamerica first encountered European explorers.  The Spaniards, led by Hernan Cortés, made friendly alliances with enemies of the Aztecs before arrived at Tenochtitlan, where Montezuma was courteous enough in his welcome but bitter about the alliance.  Soon fighting broke out between the guests and their hosts.  Montezuma was taken hostage during the unrest, and was killed in the violence, though the circumstances surrounding his death are uncertain; some sources maintain he was killed by the Spanish, others that he was killed by his own people, who were embarrassed at the ease with which their leader was overtaken by Cortés.

So we have two noteworthy Montezuma’s here – Montezuma I, who solidified the Triple Alliance between Tenochtitlan, Texcoco, and Tlacopan to form the Aztec Empire and who conquered a good portion of the surrounding lands, and Montezuma II, under whose reign the Spanish came to the Aztec Empire, and after months of peaceful cohabitation was killed in a violent clash of cultures.  Both were strong and respected rulers, who helped the Aztec Empire attain – and maintain – a well-deserved place among the greatest civilizations ever known.