The Wirral official took charge of the last ever Ninian derby and awarded a highly contentious penalty with the Swans 2-1 up in stoppage time.
Ross McCormack tumbled over a challenge from Ashley Williams and Dean pointed to the spot from which the Bluebirds grabbed a share of the spoils.
Now Jenkins is praying that history will not repeat itself when the two sides go head-to-head for the first time in the Premier League.
"I was surprised to see that Mike Dean had been appointed for this particular game," Jenkins said.
"Probably most people will say it is quite a strange choice to make, and also some of our fans might think it's a chance to put right the wrongs of what happened in the game at Ninian Park.
"But on the other hand, you have to say that every referee goes into these games and does his best.
"Every referee gives what he sees and we have to accept that.
"I just hope that in games like this - in any game - the better team on the day wins and the referee does not have to make any decisions that could change that.
"Let's hope the football decides the result on Sunday."
Although Jenkins is hopeful of securing the bragging rights in the latest Welsh derby, he insists the club's priority is to finish above their rivals come the end of the season.
"We're all really looking forward to the game - that would be the case whatever division we were in," said the Swans chairman.
"It's fantastic for the two clubs, and for Welsh football, that we are playing against each other in the Premier League.
"I think it's fair to say that neither set of supporters would have dreamed of that happening a few years ago.
"But there is always the view that whatever the result is on Sunday, it's not really going to affect our season or theirs.
"We all know what it means to the fans, but it's common sense to me that the bigger thing is to finish above them.
"Some people might disagree, but I think the majority of fans at both clubs will first of all want their team to stay up and second to finish above the other Welsh club."
Watch Cardiff v Swansea on Super Sunday on Sky Sports 1HD, kicking off at 4pm