I know it is confusing. The ship changes its time as it passes through a new time zone, both on the way out and on the way back. When there is a time change it is posted as a reminder on your navigator (just like your local newspaper reminds you to change your clocks during day lights savings time). It is also part of the Captain's announcements. They will tell you whethere to move your clock forward or back an hour. Our server also reminded us at dinner whenever there was a change. You could always check with your stateroom host or hostess to make sure you have it correct. We did the Eastern and both time changes occurred over night, so you just have to make sure you change your clock before you go to bed. But, rest assured. When you dock at Cozumel, the boat will be on local time. If it is 9 am on Cozumel, it is 9 am on the boat when it is docked at Cozumel. Hope you enjoy your swim.