Here is the key phrase:
as well as "any matters that arose or may arise directly from the investigation," according to the letter appointing him.
That's not what usually happens. It depends on how honest the AG is.
If Mueller spends months investigating something and finds nothing, he can't expand the search into other areas on a whim without permission from the AG.
Mueller is going to try to get the administration on process crimes.
Not on illegal actions but on obstruction of justice.
He's going to do things to cause a reaction from Trump, and even if Trump doesn't take the bait the press will just make shit up or publish the leaks that Mueller's office will supply them with.
All of this is under the control of the Attorney General, and Jeff Session fucked up royally when he recused himself from the investigation. He didn't need to, and what he did was figuratively stabbing Trump in the back.