When the doors open for tea-time a host or hostess will seat guests. The way tea time is run will vary by the ship's crew members working. Both times I have been to this event it was setup to where guests were served by waitstaff. However, I have heard and seen reviews that have the tea time desserts available in a mini-buffet setup. The main thing you should know is the format of the event can vary by cruise!
One thing some people may not realize is not all of the tea options are complimentary. As of the time of writing, Carnival offers regular tea, green tea, and decaf tea complimentary. If you are unsure if the tea packet is free, just ask the waiter or waitress that is serving you.
The tea packets that are not complimentary are flavored. On my Carnival Freedom cruise in 2017, the tea packets available for sale consisted of Art of Tea flavors such as: Egyptian Chamomile Caffeine Free, Mint Green Tea Low Caffeine, Black Tea Organic Breakfast Bold Caffeine, Earl Grey Creme Medium Bold Caffeine, and more. My picture of the tea packets does not clearly show the names of all of the packets available so I was unable to type all that were sold during my cruise on here.
The desserts offered can vary by ship and tea time session. Here are a few pictures I managed to capture of desserts during some of my cruises: