Generally they leave around 5pm. Manifests I believe have to be done by a certain time and from what I have heard they close the doors at 4pm. If the plane didn't land until 3:15 given that it takes roughly 15-30 mins to get bags from the flight at baggage claim, and its 45-60 minutes to the Port. I doubt they made it
If they booked the airfare through
DCL directly they may have made arrangements for them to join the ship at a later port either the Virgin Islands or Mexico depending on itinerary but not sure how late they'd hold the ship in port for late flights.
Its this situation that reaffirms for me why we would fly into a departure port the day before a cruise because we wouldn't want to risk flight delays causing us to miss the ship.