The OP has a contract with DL/AF to fly and transport his/her baggage from New York to Berlin. He has another completely separate contract with Easyjet to do the same between Berlin and Croatia. When the passenger's bags arrive in Berlin, DL/AF is basically done with their end of the bargain (until the return flight when the process starts all over again). As for why they deliver them to you when bags are delayed, that I don't know. However, my own experiences with delayed luggage and international connections did include returning to the airport and finding my luggage.

I had flown from New York to Brussels via London on BA (this was right after the liquid restrictions for carry-ons came into effect). My carry-on backpack was fine for the JFK-LHR flight, but at Heathrow a BAA employee saw my carrying it, made me put it in a sizing basket, and told me I'd have to go to check it in at a check-in counter. Mind you, my connection was departing in about 1 1/2 hours. I had to clear immigration (no check-in counters airside), clear UK customs, get to a check-in desk (Heathrow was a flippin' madhouse that morning due to a variety of problems), cut my way to the front of a security line (I'm still grateful to the long line of British travelers who graciously allowed me to bypass them in the ridiculous security line) and run to my flight as the doors were closing.

When I landed at Brussels, you guessed it-neither of my bags (my originally checked bag and my LHR surprise check) had made the flight from London. Now I'm in Brussels with only the clothes on my back. While BA did give me a travel pack with some toiletries and did reimburse me months later for some clothing I had to purchase, they did nothing else for me. I had to return to BRU the following day as my luggage still hadn't showed up at the hotel, walk into the baggage claim area and find my luggage and clear customs with it myself. There was a boatload of unaccompanied bags at BRU and BA or their luggage handling agents were making no effort to get any bags to any hotels. This may be due to each bag having to clear customs, and them not wanting to be responsible for a bag full of drugs, or it could just be that they were lazy. However, it is my belief that DL/AF will make no extraordinary effort to reunite a bag with a passenger outside of the city that they have flown into on a DL/AF ticket, particularly when it involves legalities such as clearing customs. (That is one small plus of the US system of clearing customs at your first port of entry, while you are completing immigration formalities. At least you know your luggage made it into the country.)