The Welshman had started climbing the ladder at the Liberty Stadium when Cork switched from the South Coast to South Wales.
The Jack Army academy graduate's breakthrough season came in the months that followed the England cap's arrival.
He played all-but one game for Yeovil Town in League Two during the 2015-16 campaign and followed that up with a League and Cup double with the Swans' Under 23s.
Roberts had played alongside the likes of Dan James, Oli McBurnie and Joe Rodon during that success.
"He trained with us a lot before his loans, I always saw him around the place," said Cork.
"We had a really good group of Under 23s at Swansea with him, Dan James, Oli McBurnie, there was a good group of them, they were good players, they'd come and train with us and the standards were always high.
"With the standard being so high in that group they never looked out of place when they trained with us, which has helped them become good professional players."
The Neath-born defender added temporary spells with Bristol Rovers and Middlesbrough to his resume before landing his debut for City.
The right back was handed his bow by Portuguese coach Carlos Carvalhal in a goalless FA Cup tie against Wolves at Molineux in January 2018.
And just days later he made his first Premier League appearance when replacing Mike van der Hoorn in a 1-1 draw with Newcastle United at St James's Park.
Speaking about his team-mate, who scored the fifth and final goal in Wales's World Cup qualifying win against Belarus at the Cardiff City Stadium, in what was his 33rd cap for his country,
Cork said: "He [Connor] is technically very good, his athleticism is amazing, he's a great runner and he's strong.
"He's picked up a lot of confidence through the national team, a slot has opened up for him there, he's taken it and ended up scoring a lot of goals at Swansea.
"I'm pleased to see him doing really well. He has looked sharp [in training]."
After Roberts made his Clarets debut in the Carabao Cup defeat at home to Spurs last month, Cork added: "He's had a couple of injuries, he was injured when he signed and he's picked up another little secondary injury after that.
"But he's looked good in training and hopefully we'll see him on the pitch again soon."
Roberts is expected to be involved in Wales's final Group E game at home to group winners Belgium on Tuesday evening.