As special as it was when Abreu shared time at Dodger Stadium with former Cienfuegos teammate Yasiel Puig earlier this month, this was one of the most notable gatherings of Cubans who have migrated from Serie Nacional to Major League Baseball.
"I play with you guys every day,'' Minoso told Abreu and the others on the White Sox. "Mentally. Physically, no. It's too late for me to get back on the field.''
When Abreu signed with the White Sox last October, Minoso drove down Lake Shore Drive from his North Side home to welcome him to town. Abreu thanked Minoso for blazing a trail for him and other Cubans, and Hernandez echoed those sentiments. He even used Minoso's given name to do it.
"I want to thank Orestes for what he did to lay the groundwork for us to be here,'' said Hernandez, who retired from baseball after 2007. "None of that has been forgotten by any of us. The numbers you put up in 1959, we were not able to know what you did at the big league level because the door swung shut. It's taken a lot of time for the reinforcements to arrive, but we have arrived ... and players are going to keep coming and coming [from Cuba].''
Peter Bjarkman, an American journalist who has spent much of the last two decades in Havana, agrees. He watched players like Yoenis Cespedes, Aroldis Chapman, Ramirez, Puig and Abreu play on Cuba's national teams, and he appreciates the scores of potential big leaguers still playing in Serie Nacional or on Cuba's junior teams.
"Believe me, this is still the tip of the iceberg,'' said Bjarkman, who runs the website baseballdecuba.com. "There's a lot of great talent [still] in Cuba. You're going to see more and more Cuban presence here. The White Sox have been front-runners the last few years, starting with when they added Alexei in 2008. I credit the White Sox for that.''
Unlike Abreu, Ramirez and Viciedo, Nieto was born in Cuba but raised in Miami. He's proud of his heritage and pinches himself to be playing on a team with three other Cubans. Nieto has taken to calling Abreu "the Cuban Babe Ruth,'' and it's hard to argue.
Abreu, signed to a six-year, $68 million contract, was the AL's Rookie of the Month and Player of the Month in April, when he blasted 10 home runs and drove in 32 runs. He's been in the United States only since October, but you wouldn't know he was undergoing a major transition by looking at the stats he is putting up.
But as roundtable moderator Pedro Gomez noted, it was not long ago that Abreu was going to and from games on a horse-drawn buggy while starring for the Cienfuegos Elephants. He's never far away away from that past.
"Right now I have myself [mentally] in that horse-drawn buggy in Cuba,'' said Abreu, who went into Tuesday night's game against the Giants hitting .265 with 19 home runs and 51 RBIs.
It's hard for most North Americans to comprehend the conditions that these Cuban stars left behind. At one point on Tuesday, Abreu was asked about the difference between baseball in Cuba and the United States. Hernandez jumped into the conversation.
"The primary difference is you ride around on bicycles in Cuba, and you ride in a car here,'' Hernandez said. "You eat steak here and you eat a piece of 'fried-I-don't-know-what-it-is' there. The upper echelon of Cuban baseball, without question, is equal, but you get to a point where the bottom half of the roster is not nearly the same. You're playing a much, much better caliber of baseball here. The level of respect that the athlete has in the United States is much, much higher than it is in Cuba, and that's the reality. That's how it is.''
White Sox chairman Jerry Reinsdorf is among many people associated with the team who have developed a close relationship with Minoso through the years. He last played competitively for the Sox in 1964 but did return for cameos in 1976 and '80, becoming a five-decade big leaguer.
The Sox dived back into the pool of Cuban talent in 2004, when then-general manager Ken Williams acquired Contreras from the Yankees. He doubled down on that bet by signing Hernandez as a free agent after the season.
Supporting each other and a young, inexperienced pitching staff, Contreras and Hernandez made magic in 2005. That spring, I asked the two of them what it would mean to have two Cuban pitching stars on the same team.
Hernandez said he could not put it into words, saying I should watch closely. "You will see,'' he said.
Minoso was watching from the stands during the White Sox 11-1 run through the 2005 playoffs, and he hasn't lost his appetite for his game and his team since then. If anything, the White Sox openness toward Cuban players has made him feel even better about his team and his city.
The signing of Abreu sort of sealed the love affair between the franchise and its core of Cuban players.
Hernandez said Tuesday that he made a mistake when he left the White Sox as a free agent after 2005, signing with Arizona because Williams could not guarantee him a spot in the starting rotation.
"When I did make the decision to leave the White Sox, I regretted it afterward,'' Hernandez said. "I want to ask for forgiveness from the White Sox.''
Williams, who attended the function on Tuesday, laughed and said that Hernandez earned a pardon with his performance at Fenway Park in 2005. In his greatest relief appearance, he pitched out of a bases-loaded jam he inherited to help the White Sox sweep the AL Division Series.
Ramirez used the occasion on Tuesday to say that he hopes to end his career with the White Sox. He's having his best season since arriving with a splash in 2008, hitting .311 with seven home runs and 12 stolen bases while making more than his share of spectacular plays at shortstop.
"I love it here,'' Ramirez said. "The fans treat me in a wonderful manner. They stop me on the streets and say they love the way I play.''
How will it be when the White Sox start winning with a roster filled with Cubans?
Hernandez said it best back in 2005. If you keep your eyes open, you will see.