The 3-year-old gray/roan son of Race Day also helped validate Joseph picking up his life and career and moving to the United States in 2011.
"When I said I wanted to move here, my dad said I was crazy because I had been training the best horses in Barbados," an emotional Joseph said. "But he backed me and supported me.
"After six years, I said, 'It's not going to work out.' He said, 'We've come too far to go back now. We're not turning back.'"
That determination by father and son has led to increased success in recent years, capped by White Abarrio overtaking Simplification in the stretch and holding off Charge It by 1 ¼ lengths to capture the Florida Derby at Gulfstream Park.
Charge It, under Luis Saez, finished second by a length to earn 40 points, good for 15th on the leaderboard. Simplification, the 2.30-1 favorite and winner of the March 5 Fasig-Tipton Fountain of Youth Stakes at Gulfstream, took third and picked up 20 points with jockey Jose Ortiz. He ranks sixth on the leaderboard with 64 points in all.
Classic Causeway set fractions of :23.67 and :47.24 before Simplification moved ahead soon after the half-mile.
Simplification remained in front turning for home, but White Abarrio was mounting his challenge, and secured the lead passing the eighth pole.
Whisper Hill Farm's Charge It, running greenly, made a late rally, but White Abarrio held his advantage, posting a winning time of 1:50.64 for the 1 1/8 miles on a fast track.
"I planned on being a little more forwardly placed," winning jockey Tyler Gaffalione said. "I thought Classic Causeway and Charge It would be the two on the lead and I thought we would be able to stalk them. But Jose (and Simplification) and Pappacap were pretty aggressive and I didn't want to get caught too wide, so I took back to save some ground."
Charge It entered the Florida Derby having been lightly raced. He was first and second in two career starts, both allowance races at Gulfstream.
"Super pleased with the effort," trainer Todd Pletcher said of the colt. "To get a real education in a race like that was very encouraging. He got a little green down the lane. He kind of drifted in behind (White Abarrio) and felt like if he could have just run straight that last 100 yards, he was going to be right there."
Tami Bobo's Simplification fought gamely to grab third.
"I'm so happy today," trainer Antonio Sano said of the son of Not This Time. "We made the decision to run near the front today because (Classic Causeway) was speed and (Pappacap) all the time is behind me."
Pappacap finished fourth to earn 10 Kentucky Derby points, increasing his total to 24, good for 19th on the leaderboard.
Classic Causeway, ridden by Irad Ortiz Jr., finished last in the 11 horse field.
"Irad said he thought he was traveling until about halfway down the backside and then he just sort of ran out of horse," trainer Brian Lynch said. "So, we'll do some investigating, but he looked sound. We'll regroup."
White Abarrio did not run in the Fountain of Youth following his Holy Bull win, which came after two missed works due to a fever having run through Joseph's barn.
The trainer said there also had been a "hiccup" before the Florida Derby, as the horse ran a temperature 12 days before the race.
"You wake up to that text at 3:45 in the morning, it's the worst thing you want to see because I was like not again," Joseph said. "Thankfully, he was able to fight it off. By Friday, his blood work started coming back to the point that we thought we were going to be fine."