The Hawk T1 crashed at RAF Valley in Anglesey at 1.30pm on Tuesday.
The pilot, Flight Lieutenant David Stark travelling in the aircraft is receiving medical care after sustaining non-life threatening injuries.
Witnesses reported seeing someone eject from the aircraft with a parachute before it smashed into the ground then “burned bright orange”.
Colleagues paid tribute to Corporal Bayliss, 41, describing him as motivating and inspirational.
He was part of the Red Arrows’ group of travelling support engineers, known as the “Circus”.
Sergeant Will Allen, leader of the travelling engineers, said: “Jon had the ability to motivate and inspire a team and those around him - no matter the rank, role or person.
“He was so proud to have been chosen to join the Circus team for 2018 and, in being one of the small group of engineers whose job it was to fly in a Red Arrows jet, had fulfilled a schoolboy dream.
“Jon had a big a presence on the squadron and with his wide, beaming smile, and dry humour, could lighten up any dull moment or lift spirits when needed.
“Both inside and outside of work, he was a generous, kind and caring man who could also always be relied upon.
Squadron leader Richard Bland, senior engineering officer of the Red Arrows, said: “Everyone on the team has a great story about Jon and, without exception, he was known as a top bloke with an infectious smile, cheeky grin and possessing a dry sense of humour that had the ability to fill a room with laughter.
“At the same time, Jon was the ultimate professional and embodiment of excellence.”
Corporal Baylis was born in Dartford, Kent, and grew up in Hartley and completed a course in engineering management at the University of Greenwich and worked at the Brands Hatch motor racing circuit before joining the RAF in 2001.
Before becoming a member of the Red Arrows team in January 2016, he worked on squadrons at RAF Coltishall and RAF Coningsby as well as overseas deployments.
As an engineer with the Red Arrows he had supported the team in tours of China, the Middle East and Europe.
In 2017 he worked as a leader of the Red Arrows’ dye team - responsible for refilling the jets’ smoke systems when they landed.
Earlier this year, he was promoted to the Circus team - the small group of highly trained engineers who travel with the aircraft and provide technical support to the Red Arrows when the aircraft operate away from their home base.
A police investigation and a full service inquiry into the crash has been initiated, the Ministry of Defence has said.