The group, called Mariachi Phoenix, even followed Martin into the clubhouse after the workout and continued playing while he sat at his locker.
"This is amazing," Martin said when the music finally stopped. "My teammates, my friends, my family surprised me. It's an amazing feeling to have this kind of present."
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Martin wore a sombrero throughout practice, while catching fly balls in the outfield, taking swings in the cage and running wind sprints with teammates.
"He had no problem catching the sun balls today," said fellow outfielder Jarrod Dyson.
The stunt was the latest effort by second-year manager Scott Servais to keep things loose with his team during Spring Training, and it was welcomed by the players. At least most of them. Third baseman Kyle Seager found out during the morning team meeting that he was going to be paying for the band.
"All I know is I got stuck with the bill," Seager said with a wry grin.
Martin said he had no idea who was behind the gag, but he soaked in his day and even struck up "La Bamba" with the group between hitting sessions at the cage.
"It was kind of weird swinging with a sombrero," he said, "but I was just having fun with my teammates. It was a great moment for me. This is something I will never forget in my life."
Dyson, who spent the past seven seasons with the Royals, is finding his new team to be entertaining.
"This is a great day," said the speedster who lines up next to Martin in the outfield. "It's his birthday, and the boys did something special for him. I've never seen this in my career or ever. I think it's something great to keep the guys loose on the field throughout practice.
"It probably is costing a lot of money, but it's the fun and what you get out of it that matters. And I think for Leonys, he's very happy today."
And, yeah, even the guy paying the bill figured it was well worth it.
"It's a very long season," Seager said. "And if you aren't enjoying yourself and enjoying each other, it can be a really long year. [Servais] has certainly brought a different culture here. He's made it a lot more fun, but we still have that edge where winning is the goal."
And the birthday boy was in full agreement on that.
"He's done an amazing job, everything to make this team be like a family, be together," Martin said. "That's the only way we'll get to the point we want to get."