Fortunately both players showed signs of recovery following medication, and Rudonja's diagnosis confirmed he was not suffering from pneumonia.
The optimistic mood was heightened as Milenko Acimovic, who had been sidelined through the week because of a thigh problem, resumed training on Monday.
The team's spokesman Ron Sinkovic enthused: "The situation in the team is really good right now."
The developments left the squad in buoyant mood as they left their Japanese training camp in Mimasaka for Korean base on Jeju Island on Monday.
Captain Ales Ceh made it clear that the players had benefited from the atmosphere in the training camp, which he said was thanks to their hosts.
"We spent an incredible week in Japan. We are sorry to leave Mimasaka. None of us will forget the generous hospitality we felt here for the rest of our lives," he said.
Slovenia will now prepare for their opening group B match against Spain on Sunday.
Ceh is convinced his side will be able avenge the defeat suffered when the teams met two years ago in Amsterdam.
"We are better than when we lost 2-1 against Spain in Euro 2000," he said.