It is a bit of a puzzle as to the reason for the discrepancy.

If the base is identical, and the door trim is identical, the only difference will be in the walls. And that is a problem that should be remedied.

You are quite correct. The base moulding should not extend beyond the door casing. The only exception is sometimes the shoe molding might extend further, then it should be mitred 45% where it meets the door casing or use a plinth. You said he did other work for you. Maybe he is using thicker molding to cover up mistakes. In any case, tell him the work is unacceptable and needs to be redone correctly and professionally.

Take a scrap piece of the new base and place it adjacent to the installed casing (up above the newly installed base). That will tell you if there's a difference between the thickness of the base and door casing.

Best luck with the project, rredogg