(CNN) -- Matthew Sudders has been on plenty of cruises, but he'd never seen anything like this.
The civil servant from Paris was aboard the Carnival Paradise on Tuesday when he noticed the ship had started to slow down in the middle of the Caribbean Sea. Then an announcement came over the public address system: The captain had spotted a small boat in the water, and it appeared to be in distress. The Paradise would try to help.
It appeared to Sudders that the cruise ship's captain was trying to shelter the small boat from the waves. Once they were close enough, ship staff lowered a platform down to the water and threw a rope and life jackets to the stranded craft.
Eventually, the 24 passengers from the boat, all of Cuban nationality, were able to board the Paradise. They had been stranded for five days, according to an announcement on the ship's PA system, said Sudders, one of two passengers who posted accounts of the rescue on CNN iReport.
"There was a huge cheer for the people as they came aboard," Sudders said from Grand Cayman Island on Wednesday. But he noticed a few of the cruise passengers were hesitant. Some of the people he stood next to on deck referenced Capt. Richard Phillips -- the American freighter captain whose 2009 hijacking by Somali pirates inspired an Oscar-nominated film -- hoping that the new passengers were not a risk.
He says cruise officials later informed him that the new passengers would have been subjected to security screening as they were brought on board.
The ship was en route to Grand Cayman from Tampa, Florida, when it stopped to aid the stranded boat on the first day of the cruise.
"The ship turned slowly and approached the boat," said Sudders, who was still aboard the five-day Caribbean cruise Wednesday. "The people in it were yelling in Spanish. One of them appeared to be unwell in the bottom of the boat. We could see that there was water in the bottom of the boat and although it had an engine, it was not running. As we approached the boat, one of the passengers was flagging us down with his jacket."
In a statement, Carnival officials said the ship's itinerary was unaffected by the rescue.
Ship staff provided the new passengers with food, water, fresh clothing and accommodations, and they were evaluated by the ship's medical team, the statement said. The Paradise also reported the rescue to the U.S. Coast Guard.
This isn't the first time a cruise ship has provided rescue services while at sea. Last year, another Carnival ship and a Disney ship picked up 21 people of uncertain nationality who were stranded on a raft off the coast of Key West. And in 2012, a Royal Caribbean ship rescued 23 Cubans, also near the Cayman Islands.