"We thought the co-pilot had gone mad," Francesco Cuomo, a 25-year-old development economist among the 202 passengers and crew on on board, was quoted by Italian media as saying, as fresh details about the hijacking drama emerged.
The Ethiopian locked himself in the cockpit when the captain went to the toilet during flight ET-702 from Addis Ababa, which had been due to fly to Rome.
"The captain was threatening to open the cockpit door and tried to break it down without success," Cuomo said.
"That's when we understood that something serious was going on."
After the plane touched down, Geneva police arrested the co-pilot after he scaled down a rope out of the cockpit window and prosecutors said the chances of his asylum demands being met were slim.
In an audio recording on Italian media websites, a voice said to be the captain could be heard trying to reassure passengers once they were on the ground.
"The pilot is still locked inside the cockpit but he is not armed," the man is heard saying.
"He threatened to crash the plane," the voice continues.
"I don't know his motives and I'm not interested — all I'm interested in is the fact that you're safe."
In a smartphone video also on Italian media, passengers could be seen with their hands behind their heads as a police announcement is heard over loudspeaker repeating: "This is a police operation. Do not move!"
Addis Ababa identified the co-pilot as 31-year-old Hailemedehin Abera Tagegn, who has been working for the airline for five years.
He told police "he felt threatened in his country and wants to seek asylum in Switzerland," Swiss police spokesman Eric Grandjean told AFP.
Fighter jets scrambled
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A total of 202 passengers and crew were on board the Boeing 767 as the drama unfolded.
"The co-pilot told air transport authorities he had a problem with his plane and needed to fill up with jet-fuel. He then set off a distress signal indicating the plane was hijacked, before saying he had engine trouble," Grandjean said.
Head of operations at Geneva airport, Xavier Wohlschlag, told the ATS news agency the hijacker's request to land was initially denied.
The green light was not given until around 5:30 am (0430 GMT), as the passenger jet, which was first escorted by Italian fighter jets and later reportedly by French ones, circled the region.
It emerged later on Monday that no Swiss fighter jets were scrambled as the hijack happened outside the business hours of the country's airforce, which operate between 8am and 5pm.
The plane finally landed in Geneva at 6:02 am, about an hour and a half after it was due in Rome.
"He parked the plane on the taxiway, he cut the engines then opened the cockpit window, threw out a rope and used it to descend to the tarmac," Grandjean said.
"He ran towards the police and immediately identified himself as the co-pilot and hijacker."
Tagegn said he acted alone, but as a precaution all those on board were frisked as they left the plane.
The runway was crowded with police and other emergency vehicles as passengers filed out with their arms up in the air or on their heads before boarding waiting buses.
Geneva's chief prosecutor Olivier Jornot said Tagegn's reasons for feeling in danger in Ethiopia were unclear as he had not expressed any "political or other motives" and an asylum claim seemed unlikely to succeed.
"His chances are not very high," he told reporters.
The man risks a 20-year prison sentence.
Flights to and from Geneva were either diverted or cancelled during the drama, but operations later resumed, said airport chief executive Robert Deillon.
Up to 30 flights and 4,000 passengers flying during the busy ski season were estimated to be affected.
The last time a hijacked aircraft landed in Switzerland was in 1995, when a Spaniard hijacked a Majorca-Paris flight to protest at France's Pacific nuclear testing.
All on board were unharmed, and the man was ruled to be mentally ill.
In all, 14 hijackings have occurred in Switzerland since 1969, when Arab militants seized an Israeli passenger plane at Zurich airport, fatally wounding a pilot.
One hijacker died in a subsequent assault by Israeli special forces and three others were arrested.