The Esks host their former long-time quarterback and the Toronto Argonauts on June 30.
Tillman traded Ray to the Argos in a December blockbuster deal for quarterback Steven Jyles, kicker Grant Shaw and a draft pick.
"Ricky is one of the more beloved players in club history," Tillman said Thursday during a CFL conference call. "I think he's going to be embraced.
"There's no pressure on him. If there's pressure that day it will be on me."
The Eskimos head into training camp with questions at quarterback. Can Jyles carry the freight for a whole season or will veteran Kerry Joseph be required to step in?
"Ricky Ray is a future Hall of Famer and when you trade a Ricky Ray there will be questions and we understand that," Tillman said.
Even if Ray's performance in Edmonton on June 30 makes Esks fans wish him back, Tillman says the trade was a move he had to make now for the long-term health of the Eskimos.
Ray, 32, is an expensive player under the $4.35-million league salary cap, he says. Tillman felt it was better to move him prior to the 2012 campaign, instead of waiting until 2013 or 2014.
"We would have had a ton of free agents because we still would have had the highest-paid quarterback in the league, the highest-paid player in the league on our payroll," Tillman forecasted. "We would not have the ability to extend some contracts and maintain our nucleus.
"Could we have waited another year or two? Yes, we could have, but a year from now, Ricky would be turning 33 or 34. If the trade doesn't work, that's my responsibility.
"It was about having the confidence in our young guys that somebody would step forward. It was about creating cap space and feeling that there's never a good time and it's probably better to make the change before it's obvious to everyone the time has come to do so."
Training camps open June 3 for all CFL teams.
Jyles, Joseph, Matt Nichols, Eric Ward and Jeremiah Masoli will be the five signal-callers in Edmonton's camp, but the battle for starter is expected to be between Jyles and Joseph.
Jyles, 28, has 20 career starts over six CFL seasons and has thrown as many interceptions (29) as touchdowns (31). He compiled 2,804 passing yards in 16 games, including 11 starts, with Winnipeg in 2010.
Jyles got the ball in Toronto for eight games last season when Cleo Lemon was released and the Argos were well out of playoff contention. He completed 124-of-218 passes for 1,430 yards with seven touchdowns and 11 interceptions.
Joseph, who turns 39 in October, won both a Grey Cup and the CFL's Most Outstanding Player award in 2007 with the Saskatchewan Roughriders. Two unsuccessful seasons in Toronto after that, Joseph then joined the Esks as Ray's backup.
"We believe Kerry can be a starter," Eskimos coach Kavis Reed insisted. "Kerry will come in and compete for that starting position.
"I think Kerry is a 39-year-old quarterback with a 24-year-old's body. We're not at all concerned that if he wins the job, he cannot survive through an 18- or 20-game season."
The Eskimos are coming off an 11-7 season in 2011, good enough for second in the CFL's West Division.
Edmonton beat Calgary 33-19 in a playoff game at Commonwealth Stadium before falling 40-23 to the host B.C. Lions in the West final.
"You've never heard us use, and you never will hear us use, the term re-build," Tillman said. "We have high expectations.
"At this time last year, most people picked us last."
Another key position Edmonton must sort out at training camp is at running back following the departure of Jerome Messam, who was the CFL's outstanding Canadian. The Toronto native signed with the NFL's Miami Dolphins in February.
Calvin McCarty, Hughes Charles, John Goebel and newly-signed Cory Ross are prospects to try to fill that void.
"We think we've got four interesting competitors and we'll just let it play out," Tillman said.
Edmonton will get one of their two first-round draft picks this year to camp. The Philadelphia Eagles didn't extend a contract offer to Wilfrid Laurier's Shamawd Chambers after a mini-camp, so Tillman expects his No. 6 pick in Edmonton.
Offensive lineman Austin Pasztor, taken No. 4, has signed with the Minnesota Vikings.
Edmonton had the second-best defence in the CFL last season. Reed predicts the Esks' pass-rush will be the centrepiece of the defence, led by defensive lineman Marcus Howard.
The off-season signing of lineman Rashad Jeanty is a blast from Edmonton's past. Jeanty won Grey Cups with the Esks in 2003 and 2005 before heading to the NFL.
"If he is 50 per cent of what he was when he left to go to the NFL, he's going to be a gentleman who is going to pose a lot of problems for offensive linemen," Reed said.
A major change in Edmonton's coaching ranks was the promotion of Mark Nelson from linebacker coach to defensive co-ordinator with the departure of Rich Stubler to the B.C. Lions.
"There won't be that much of a difference between Rich Stubler and Mark Nelson philosophically," Reed said. "Schematically, there may be some noticeable differences."