If you are flying into Germany from outside of the Schengen zone (like from the US), you'll go through Schengen immigration (passport check) in Düsseldorf. If you have carryon luggage, there will be a customs line there, but if you have nothing to declare, you should be able to just walk out through the "nothing to declare" line. If you have luggage checked through, you won't see it until you get to Nürnberg.
I've only flown out of Düsseldorf to the US. Both flights were Lufthansa, in the same terminal. I just went down the hall to the international departures end of the building, passing through outgoing Schengen passport control in the hallway on the way, but I don't know how they handle incoming international flights.