Once the engines are ignited and liftoff occurs, are any operators/controllers on the ground making any manual changes to the flight? Or are they simply monitoring the entire event until the boosters return to earth?
The rocket is autonomous, it flies itself.
The navigational math, engine, and flight dynamics of a Earth-based orbital class rocket in operation are far too complex for manual operation, especially remote manual operation. Even simpler rockets (like Apollo LEM) that could be flown manually have still attempted to offer automatic operation in the interests of safety and reliability.
Ground control retains the ability to send a destruct command, and they are able to directly control events after the dynamic period ends and the upper stage is in orbit - for instance, delaying payload deployment until receiving the all-clear from the launch team and payload team.
Elon Musk made reference to the "Holy Mouse Click" that happens right before they start loading fuel. From that point forward, the rocket will launch itself at the planned time, about 2 hours in the future, unless something happens that stops it prematurely. I'm not sure if there are other prompts that are required, but things are pretty automatic.
In fairness, pretty much every rocket has been automated since they started launching them. There just isn't the time or precision to manually control them. Even the Apollo moon landings were only semi-automated, controlling where to land, but not firing the rockets directly.
There are several levels of automation on a SpaceX launch.
Strictly speaking, full control to the rocket is only given 60 seconds before launch (start up sequence, look at any SpaceX launch webcast). Without, the rocket won't launch even if T-0 is reached without a single warning. With it, the rocket will launch on its own at T-0 unless the rocket itself detects a problem. Humans can still intervene up to a few seconds before the hold downs are released (even after engine startup happens, but at that point there shouldn't be any problems, just as a last resort emergency tool).
But even before that, ground computers handle various flow sequence items, including loading LOX/RP1 into S1 and S2, removing that if the launch is a no go or after a static fire, and several other things.
A human being simply don't stand next to a launch pad, after rocket loading is started. Actually even 30 minutes prior, its a no go, unless there's something wrong and the computer controlled operations are disabled for people to go fix something.
The Elon Musk holy mouse click means giving the ground computers control over the general pre launch flow. But humans are monitoring all events like a hawk until lift off. Its a redundancy of both the computer itself monitoring things as well as humans.