Help!!!! Any Past Conquest Cruisers Do Dolphin Swim in Cozumel???

I went to the Carnival website & it says we are arriving in Cozumel at 10:30 AM and depart at 6:00 pm. Is this Cozumel time?

I booked the dolphin excursion online because I want to make sure it doesn't get sold out. We want to do the Royal Swim which should take an hour (maybe longer if they are running behind) but also want to have time to do shopping and go to Carlos and Charlies too.

The times I had to choose from was 12:00, 2:00, 3:30. I'm scared to do the 3:30 beings if they are running late. I just figured if we can get to the 12:00 easily, without being pressed for time to get there (we have to be there for 11:30 as per the email I received) that would give us the rest of the day to do whatever we wanted to do. Will we get to Cozumel at 10:30??? Do they run late sometimes? If the Carnival website says 10:30 AM are we really not getting to Cozumel until maybe 11:30 or something like that? Should I just change our reservations to 2:00? So, so sorry for all the question, just didn't know where else to turn.........this board is so helpful !!!

On all the Carnival cruises I've been on the Captain has kept the clocks on the port of embarkation (IE Tampa or Miami time). Therefore if you go into another time zone then you have to take account to that. So if you are going to be in Cozumel at 10:30am then that is 10:30AM of the port you left from. I think Cozumel is CST so it would be an hour earlier in Cozumel if you left from an EST port (FLorida port). Therefore you'd be docking at 9:30am Cozumel time which would give you plenty of time to make a 12pm tour.