The cruise lines block air at negotiated rates with the airlines, but the airline generally decides which flights they will provide for the cruise passengers (unless you do an air deviation). It is not uncommon for folks on the west coast using the cruise line's air for a cruise departing from Florida, to connect through Chicago, or some other airport that might have weather delays in the winter time.
While the cruise line arranges the air, they do not guarantee that you will make it to the ship. That is between you and the airline, as far as they are concerned.
You are always much better off taking charge of your own airline reservations to make sure that you and your luggage get there in plenty of time. I would never fly in for a cruise on the day of departure (unless there were multiple flights and it was a short distance. Even then, I would still go in the day before so that I can get a good night's sleep, have a nice breakfast and then make my way to the cruise terminal and be one of the first on the ship to start my vacation.
Hope that helps.