How did the Neo-Assyrians control their empires?

The Neo-Assyrian Empire is a term used to describe the leading power in Mesopotamia between 911 and 612 BC. Structurally, the Neo-Babylonian Empire followed the administrative patterns evolved in the Neo-Assyrian period. It was an empire notable for developing many of the tools of power and control used by subsequent great Middle Eastern empires such as that of Persia and Alexander's successors. 
One important strategy was handling territorial acquisitions by organizing different regions into provinces, each with its own governor and responsible for providing a fixed amount of taxes and military forces to the king. 
Another important strategy was the system of deputies, which created a clear administrative hierarchy and succession of power on all levels. As the deputies were normally appointed by the king rather than by their nominal superiors, they also created a check on the power of various officials. The king himself had seven major officials directly under him: commander-in-chief, treasurer, chief cupbearer, chief eunuch, palace herald, vizier and chief judge; each of these had a deputy. If an official needed to travel or was incapacitated, the machinery of administration did not come to a halt as the deputy would automatically step into his place. 
Next, the Neo-Assyrians had a highly trained standing army in which foreigners and tribute soldiers from vassal states were fully integrated. The development of a large, well-maintained transportation and communication network (and massive road building) meant the army could quickly be deployed where it was needed. 
https://www.ucl.ac.uk/sargon/essentials/governors/thedeputysystem/