Flight connections

too tight; the flights are always late but if you book all one airline they will put you on the next one Zurich to Dubrovnik if there is one.
also your bag might get lost on such a tight connection if you are checking it

As best I can tell, you are looking at booking separate flights.

The proverbial snowball in Satan's residence would get better odds.

We are looking at a flight from Zurich to Dubrovnik arriving from Phil
into Zurich at 850am and leaving for Dubrovnik at 1005. I am worried
that this is too tight a connection, as I assume that we will have to
go through immigration in Zurich.

If the one-ticket itinerary is from Philly to Dubrovnic and you miss the connection to Dubrovnic, you'll be put on the next available flight. Airlines don't sell tineraries in which there is a strong likelihood you'll miss the connection to your destination. There is a minimum connection time. 75 minutes is tight.

Now if you're talking about two different tickets one transatlantic and the other intra-European on separate itineraries, you need to allow 3-4 hours because if you miss the intraEuropean flight, you forfeit the return flight to Zurich assuming you want to buy a roundtrip between Zurich and Dubrovnic to catch the flight home to Philly at the end of your trip. Two different itineraries is NOT a connection.