Still, before he could take a deep breath, young Mariners prospect Francisco Martinez laced a sharp line drive right down the line that Jaso instinctively dove for and gloved like he'd been doing this every day of his life.
"The day before the intrasquad game, I took some grounders at first, but none of them were hit nearly as hard as the one he hit at me," Jaso said. "Other than that, I would take grounders here and there with the Rays, maybe once a month or every other month."
The Mariners are looking for some versatility from Jaso, however, as a potential third catcher behind starter Miguel Olivo and top prospect Jesus Montero. They'd like to find more ways to use him, which is why the 28-year-old from Chula Vista, Calif., certainly isn't going to argue with being asked to try some new things.
"If they want it, I want it," Jaso said.
What the Mariners want is to find ways to get something out of a catcher who was athletic enough to bat leadoff at times for Rays manager Joe Maddon.
That won't happen in Seattle, where Eric Wedge has Chone Figgins and possibly Dustin Ackley in mind for filling that role now that he's moved Ichiro Suzuki to third in the order. But Wedge also likes Jaso's solid .340 career on-base percentage, as well as his approach.
"He's kind of a baseball rat," said Wedge. "His uniform is going to be dirty. He's easy to talk to, he understands the game. You can tell he's been paying attention over the years with regard to knowledge and feel.
"I put him out at first base [Sunday], because I want to see if that's another option for us with regard to versatility. There's going to be some pinch-run situations. He can run a little, he can catch. If he can play some first base, too, that's great. He puts up a good at-bat. He has some tools, he has something to offer. I've been impressed here early on."
Having played for the unorthodox Maddon, Jaso is used to being ready for anything. He remembers the day he walked into the visitors' clubhouse in Yankee Stadium and saw his named penciled in third in the lineup.
Same thing happened when he started batting leadoff for a run of games in 2010. Nobody told him in advance, he just showed up and saw his name in the top spot 41 times that season, just the third catcher since 2001 to leadoff in that many games in the big leagues.
"I don't think I'd hit leadoff my entire life," he said. "Little League, high school, never a leadoff guy. Then all the sudden, Major League Baseball, that's what it took, I guess. Or it took Joe Maddon. One of the two."
As for his new skipper? Wedge is correct in assessing Jaso as a baseball junkie.
"Baseball was the only sport I knew," he said. "I played a little basketball here and there, but once I got to high school, it was all about baseball."
His love for the game stemmed from his relationship with his grandfather, Michael Bajo, who played a little pro ball himself before deciding to go to medical school to become a doctor.
"We were close, so I was always talking to him and that kind of made my passion grow," said Jaso. "He was kind of living through me. He definitely wanted to go back and keep playing baseball if he could, so I was his outlet for it and it made my love for the game grow even more. It being so important to him made it more important to me to keep going."
Jaso's grandfather died in 2008, shortly after he was promoted to the Major Leagues after six seasons in the Minors.
"He got to see my first hit on TV, then he passed away about a week later," Jaso said. "That's what he always told me, 'If you make it to the big leagues, then I can finally die.' So it's kind of a sad thing. But that was always something to keep me motivated coming up through the Minor Leagues.
"There are so many times you have doubts and money is tight and you're wondering if you're doing the right thing for your life. Those thoughts would go through my head like twice a season coming up. I spent a lot of years down there. But having him and people like that where it meant so much for me to be doing what I'm doing, it helped me get through those hard times mentally."
Now he's adjusting to a new situation, having been acquired by trade for reliever Josh Lueke in November, only to learn a month later that the Mariners had dealt for Montero as well.
Jaso figures nothing has changed, he's still fighting for a spot on a team that guaranteed him nothing more than a chance.
Regardless of his own situation, he's intrigued by what he sees going on around him this spring.
"I like it here," Jaso said. "This team is growing, and it's growing in the right direction. I really like the feel of the clubhouse. The front office seems to have done a really great job of getting the right attitudes together and keeping the bad ones out. This is a good developing atmosphere for all the young talent here. And there's a lot, especially in the pitching category."
Jaso played on playoff teams with the Rays in 2010 and '11. He'd love to stick in Seattle long enough to see similar success.
"Yeah, coming up in Tampa, all our Draft picks were finally making it up there and doing good," he said. "It's a matter of time and adding a little leadership here and there and you'll get yourself a pretty good team."