Time on ship or time on port

I am taking a 7 days cruise to eastern Caribbean, but does NCL Escape stay on Eastern Time or Central while visiting the (Cozumel, Belize, Costa Maya and Roatan) or does the ship changes time to match port of call time:

Cozumel (Central Time)

Costa Maya (Central Time)

Belize City (Mountain Time)

Roatan (Mountain Time)

Thank you

Time always matches the port. You will get a message (usually a card) in your cabin the night before to remind or alert you of a time change.

Didn't Cozumel switch to Eastern time recently? I know it switched times zones, but I am unclear. I never worry about it though as the ship crew will let you know if you pay attention.

i have been reading about but when i looked up the current time, it tells me is on central time.

thank you.