A military rescue crew in Florida has spoken of the “pretty miraculous” survival of all 11 people it saved from a plane crash in the Atlantic Ocean, and its own scramble to safety with five minutes of fuel left.

Members of the 920th rescue wing, based at Patrick Space Force base, not far from Cape Canaveral, raced on Tuesday to reach the passengers and crew in choppy seas. They had emerged from a small Beechcraft twin-propeller aircraft that ditched into the water about 80 miles east of Melbourne on Florida’s east coast.

By the time their rescuers arrived, in a Combat King II transport plane and a HH-60W Jolly Green II helicopter, the survivors – all Bahamian adults – had been packed into the only tiny life raft they had, for about five hours. There was no sign of the plane or any wreckage, and the first responders said the passengers would have had no idea that help was on the way.

“I’ve not known anyone to survive ditching in the ocean,” Maj Elizabeth Piowaty, the transport plane’s pilot, told a press conference at the base on Wednesday.

“And from what I’ve seen, for all those people to survive is pretty miraculous, and then get in the raft all together.”

Over almost an hour and a half, using a winch and basket, the helicopter crew made nine lifts in choppy seas to get all the survivors onboard, then fly them to waiting ambulances at Melbourne airport.

Lt Col Matt Johnson, who piloted the helicopter, revealed that his aircraft had only about five minutes of available fuel remaining for the rescue operation when the last of those in the raft was hoisted up.

He told reporters that moment was “bingo time”, a colloquial military term for the “hard time that we need to leave the scene and go back because we’re low on gas”.

His helicopter, he said, had the capability of in-flight refuelling “if we exceeded our bingo fuel and we’re running low”, but the operation would have delayed getting the survivors, some of whom needed urgent medical attention, to shore.

“We did not need to do that yesterday, but we were ready to go,” he said.

Piowaty said an incoming thunderstorm added urgency to the search, which was initiated by an alert from the plane’s emergency beacon that activated on impact and was picked up by the US Coast Guard.

The aircraft was reportedly on an internal flight between the Bahamas islands of Marsh Harbour and Grand Bahama when it ditched. The cause of its sudden emergency is under investigation.

Air force Capt Rory Whipple, one of the crew members who was winched down to the life raft, said the survivors “were in distress, physically, mentally, emotionally” after so long in the ocean, unaware of whether there was any possibility of a rescue.

“They didn’t even know that we were coming until we were directly overhead,” he said.

“So you have to imagine the emotional injuries that were sustained out there and not knowing if someone was going to rescue them. But that’s our job. We have the best job in the world, on someone’s worst day we are at our best to bring everyone home.”

One of the survivors, Olympia Outten, was a passenger on the plane, travelling with her son and her niece. She said it appeared that the pilot got off course in stormy weather, fuel was running out and the plane had to ditch in the sea.

“I was trapped, I had my seatbelt on, my son was saying ‘Mummy, go’ we had to get out,” she said, in an interview shown on CNN on Thursday. Then she began sobbing. Her son helped free her and, when in the water, she kept telling herself, “God, save us, let someone see us,” Outten said.

When the US aircrew, who had been doing water rescue training in the area, responded to the plane’s signal, she said the survivors felt joy. The swell was increasing up to 5ft and storms were imminent when the survivors were rescued. No official account of what caused the plane to go down has yet been given.