I have started learning concurrency and threads in Java. I know the basics of synchronized (i.e. what it does). Conceptually I understand that it provides mutually exclusive
Assuming each thread passes a different array then no synchronization is needed, because the rest of the variables are local.
If instead you fire off a few threads all calling sortA and passing a reference to the same array, you'd be in trouble without synchronized, because they would interfere with eachother.
Beware, that it would seem from the example that the getList method returns a new List from an array, such that even if the threads pass the same array, you get different List objects. This is misleading. For example, using Arrays.asList creates a List backed by the given array, but the javadoc clearly states that Changes to the returned list "write through" to the array. so be careful about this.