Jones revealed on Tuesday he would step down as Japan boss following the Sept. 18-Oct. 31 tournament in England after revealing last week he was "chatting" to South African Super Rugby side Stormers about a role.
Katsuyuki Kiyomiya, who coaches top flight side Yamaha Jubilo and worked alongside Jones previously at Suntory Sungoliath, accused the former Australia boss of lacking respect.
"You have to wonder about the timing of the announcement," Kiyomiya told Nikkan Sports.
"It's not something you do just before the start of the World Cup.
"It's outrageous for him to be thinking about his next job when he's got the World Cup right in front of him. He must think we're all fools."
Kyodo News said that Kiyomiya had long declared his interest in succeeding Jones.
Japan, whose only World Cup win came in 1991 against Zimbabwe, have been drawn in Group B for the tournament alongside South Africa, Samoa, Scotland and the United States.
(Writing by Patrick Johnston in Singapore; editing by Amlan Chakraborty)
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