Hi Kendall,
Yes, they keep the same time as in Fl. As for alarm clocks, I've never seen one in any of my cabins, but the do have set a wake-up call if you want, have used that and it worked out just fine.
Yes here in Tampa we are on eastern time and I would take a travel alarm clock on your cruise. I know I plan on it. Happy cruising!! Hope you enjoy Tampa while you are here!!!
We didn't have a clock in our room at all, so we were very glad that I threw the digital alarm clock in the bag at the last minute. The digital clock was nice because with an inside cabin it stays pitch black until you turn a light on no matter the time of day. We would of missed several excursions without it.