Archer threw six solid innings, Evan Longoria hit a three-run homer and the Rays split a four-game series with Toronto by beating the Blue Jays 7-2 on Thursday night.
Archer (1-0) allowed two runs, four hits, two walks and had seven strikeouts. Archer and the Rays agreed to a $25.5 million, six-year deal Wednesday.
"The conversations he and I have been having, I thought it was going to be OK," Maddon said. "He's been really kind of matter-of-fact in a good way about all this stuff."
Archer's contract includes club options for 2020 and 2021 that could raise the value to $43.75 million.
"Having it or not having a contract or money, it didn't affect me because it's never been a thought in my mind when I was in between the lines," Archer said.
Longoria tied Carlos Pena for first on the Rays' career home run list with 163 on his seventh-inning shot off Esmil Rogers that put Tampa Bay ahead 7-2.
"It's a proud moment for me because this has been my home for so long," Longoria said.
Brandon Morrow (0-1) gave up four runs and seven hits over five innings in his first start since May 28.
The right-hander missed the final four months last season due to an entrapped radial nerve in his right forearm.
"That was a tough one where you feel like you pitched better than the line," Morrow said. "But to their credit, they didn't give away any at bats, worked counts, and found those holes when guys were on and got their runs."
The Blue Jays extended their winless road series streak at Tampa Bay to 21. Since taking a series in April 2007, Toronto has lost 19 and split two road series against the Rays.
"Against those four starters they threw at us, to get two wins, you've got to feel good, especially after getting knocked around a little bit that first game," Toronto manager John Gibbons said. "So we'll go home feeling good."
Ryan Hanigan had an RBI single in the second, and Desmond Jennings hit a run-scoring double during a three-run third as the Rays took a 4-0 lead.
Toronto got to 4-2 in the fourth on Dioner Navarro's sacrifice fly and an RBI infield single from Brett Lawrie.
Tampa Bay right fielder and 2013 AL Rookie of the Year Wil Myers was scratched from the lineup due to flulike symptoms. Infielder-outfielder Sean Rodriguez was placed on the paternity leave list for the birth of his son and infielder Vince Belnome was recalled from Triple-A Durham.
With Rodriguez expected back Friday, Belnome was optioned back to Durham after the game.
Rays outfielder David DeJesus returned after missing the previous two games with a bruised right foot and went 2 for 5. First listed to start in left field, DeJesus was moved to designated hitter.
Gibbons wanted to challenge an out call on Lawrie's one-out grounder in the ninth, but was denied the opportunity because he was too late in telling the umpires of his decision.
"Once the pitcher steps on the rubber and the hitter steps in the box, they nullify it," Gibbons said. "It turned out he was out, but at the time it was questionable."
NOTES: Toronto closer Casey Janssen, on the 15-day disabled list due to a strain in his left abdominal area and lower back, continues throwing on level ground. The right-hander doesn't know when he will have a bullpen session. "We're just trying to work our way to the mound," Janssen said. "Want to get comfortable on flat ground." ... Tampa Bay RHP Jake Odorizzi and Texas LHP Joe Saunders will start the opener of a three-game series Friday night. ... The Blue Jays will start RHP Dustin McGowan in Friday night's home opener against the New York Yankees. Japanese star Masahiro Tanaka will make his major league debut for the Yankees.