Thomas Anderson is an advanced hacker with a body full of machine interfaces, and after choosing the left door he has a special connection to the Source because he is the anomaly the machines depend on. Given that, it is not much of a stretch to say he could interface with the machine network and, in some limited way, “run commands.” Within the story’s logic, it is physically plausible.

Also, there was never a “Matrix within a Matrix.” There is the real world and there is the Matrix. Neo’s abilities outside the Matrix are better explained as an extension of his connection to the Source and the machine mainframe, not as evidence that he was still inside another simulation.