It is important to recognize different time frames for the expected responses from individual generation units and from the power control center regarding balancing generation and load. The key variable here is the system frequency. If the frequency is below synchronous, you have too much demand for the available generation while frequency above synchronous indicates more generation than demand.
In the example of the outage of a 600 MW generator, frequency will initially drop at a rate that is related to the total inertia of the remaining generation units synchronized to the grid. All prime movers are equipped with speed governors that will sense the frequency drop and will react by increasing the mechanical output of the prime mover (opening gates in hydro units, opening valves in combustion or steam turbines, etc.). This is an automatic response and it is decentralized, not part of the functions of a power control center. The speed governors usually curb the frequency drop in a few seconds (5 to 10 seconds) and raise the frequency back towards the synchronous frequency (50 Hz or 60 Hz). A new steady state condition is usually achieved (if enough spinning reserves are available) in many seconds, something like 30 seconds to a 60 seconds. This is often called the primary frequency control of the system.
But speed governors HAVE to operate with speed droop (it is a stability requirement, if all speed governors were trying to bring frequency back to synchronous they would "fight" each other) and, because of droop, frequency will not recover all the way back to synchronous.
Then, the power control center will be responsible for restoring frequency back to nominal. This can be done manually by the system operators or could be an automatic function usually known as Automatic Generation Control (AGC). This is often called the secondary frequency control of the system. In North America, this has to be achieved in less than 15 minutes, so only limited (specialized) types of generation reserves can be used, those kinds of generation units that could be started up, synchronized to the grid and ramped up in power faster than this threshold of approximately 10 minutes to 15 minutes.
Beyond the secondary frequency control (AGC), the power control centers usually run generation unit commitment or similar market functions that determine the generation units to be dispatched, often looking 1 hour ahead up to 24 hours ahead in time, based on forecasts of the system demand.