"He'd say, 'No, no, no, you need to get a glove, you need to get a bat and ball,'" Castillo said, retelling the story and laughing. "He said, 'You have to play baseball.'"
Now Castillo does, and he thanks his grandfather every day for helping him start his career.
Baseball is joining in the celebration of National Hispanic Heritage Month, and the tremendous impact of players from all over Latin America has been felt with every Major League team.
The game was an important part of Castillo's life in the Dominican Republic. Rodriguez, Castillo's uncles and his father all played on organized teams, although none made it to the U.S. Major Leagues. Castillo, who grew up in San Isidro, which is near the capital city of Santo Domingo, would spend a couple months with his grandfather each year. Castillo would play with other kids in the streets, using a rolled-up sock as a ball and whatever stick they could find as a bat.
With his grandfather's gift of equipment and his encouragement, Castillo learned the game, joining the adults on the diamond. It became fun, and he eventually convinced his father to sign him up for Little League.
Castillo was an infielder at the time, although he will admit he wasn't the fastest on the field. It was his bat that others noticed. He was invited to a tryout at the Cubs' facility in Boca Chica. There were five other catchers in the group of 70 players. Jose Serra, the coordinator for Latin American scouting for the Cubs, watched as Castillo threw the ball around the infield, then asked him to put catching gear on and get behind the plate.
"The first pitch I caught, I dropped -- I dropped every pitch," Castillo said. "Serra said to my manager, 'What happened?' [My manager] said, 'He was an infielder. I made him a catcher a couple days ago.' I was so scared. I didn't know how to catch."
Serra saw something and wouldn't let Castillo go home for a change of clothes after his workout. The Cubs were worried that if the youngster left the facility, a scout from another team might try to sign him. Oneri Fleita, then the Cubs' head of player development, saw Castillo play a few days later, when Castillo went 5-for-6 with two doubles.
"But I was terrible behind the plate," Castillo said.
Of the 70 players invited to the tryout that day, the Cubs signed two, including Castillo.
Castillo's manager wanted the teen to hold out for more money. In the Dominican, the manager or scout -- also known as a buscone -- often gets a share as a reward for bringing the young prospect to the big league team. Castillo just wanted a chance to play.
"I said, 'I don't want to lose this opportunity,'" Castillo said. "At that time, you don't know if you're going to make it, because too many things can happen. That was my dream. I put my heart into it. I got early work and extra work, because I had to learn how to catch."
He was 17 years old when he signed on Dec. 8, 2004. Whenever he sees Serra, Castillo reminds him of that tryout. Serra also signed Cubs shortstop Starlin Castro, at 16.
"Castro had the ability to play, but he was really skinny and no power," Castillo said. "[Serra] can see the future. He'll say, 'What can you do, what kind of player can you be?'"
Castillo had never had more than 20 big league at-bats prior to this season. Now, he's sharing time behind the plate with Steve Clevenger. There's still a lot to learn. On days when Castillo isn't catching, he often gets some extra lessons with Cubs coach Mike Borzello. They are tweaking everything, from Castillo's arm angle to how he frames pitches.
"Everything he tells me and teaches me makes sense," Castillo said. "It helps make the pitcher feel better with you."
And when Castillo isn't in the game, he tries to get next to Borzello in the dugout to ask questions.
"I want to catch a World Series some day, especially with the Cubs," Castillo said. "I want to be part of it. That's my dream. I want to be part of the team that wins the World Series. I want to be the best I can to help the pitching staff and help the team win."
Whenever Castillo returns home to the Dominican and is reunited with his uncles and relatives, he reminds them of those days when he was 7, and they played baseball for fun. Only his parents and younger sister have made it to the U.S. to see Castillo play. Someday, he hopes to bring one of his older sisters, Evelyn, because she always supported him.
"I'll never forget where I come from," Castillo said. "I won't get lazy or think it's safe. I need to work harder. I want to be here all the time. There are other guys who want my job. I have to do my job and work every day. I have to work like every day is the first day."
Rodriguez would be proud. He never got to see his grandson play in the big leagues. Rodriguez died when Castillo was 13.
"I think he was the No. 1 person to motivate me to play baseball," Castillo said. "I wish he would've been able to see me play. I know he's watching. I know he'd be really proud. That was [my grandfather's] dream -- that I would be a professional baseball player."
Carrie Muskat is a reporter for MLB.com. She writes a blog, Muskat Ramblings, and you can follow her on Twitter @CarrieMuskat. This story was not subject to the approval of Major League Baseball or its clubs.