Confirm ship time and island time in January?

I have a 10:00 am excursion planned for January but don't have FTTF for Carnival. If our ship docks at 9:00 am, island time will also be 9:00, correct? Trying to figure out if I will be able to make it to the meeting location by 10:00 island time.

You'll make it fine. If the ship changes time, they will tell you...and ship's time is the ONLY thing that matters. Your private tour guide understands how this stuff works....they will wait.

In January and the winter months, Island Time is the same as Miami time. Assuming your ship departs from Florida then there should be no time difference.

However Cayman does not (yet) observe Daylight Savings Time. When most the the US leaps forward in the spring the clocks in Cayman do not change.

There has been a (very) little discussion recently about adopting DST in Cayman. Probably won't happen anytime soon.