The now 21-year-old was six when his father, former pro pitcher Gabriel Rincones Sr, announced he was uprooting the family from Venezuela to Glenrothes, where he had found work as an offshore safety adviser in the oil industry.
Rincones Jr had been playing the sport since he was a toddler but saw no cause for concern when it came to the impact of the move on his big-league dreams.
“I was told I was going on vacation,” he told the PA news agency about the original move.
“But it’s great, because my makeup, all the relationships I’ve built over there, are irreplaceable.
“I didn’t play baseball (in Scotland) but I picked up swimming, judo, I got to call myself a Scot. Obviously I get to talk (with an American accent) now, but that’s not how I originally learned to speak English. Now it’s just to fit in here.”
To prove his point, Rincones Jr, whose passport also allows him to compete for Great Britain’s national team, switched his accent, something he says is easy for him to turn on and off.
Occasionally echoes of his six boyhood years in Fife even slip naturally into Rincones Jr’s speech, and he consciously switches words like “rubber” and “rubbish” for their American equivalents depending on his location.
The 6ft 4in left-handed hitter was the Phillies’ second pick of the MLB draft, going 93rd overall in the third round to put him in line for a 659,800 US dollar (£549,979) signing bonus.
His mum, dad and two sisters are still based in Scotland and his parents, who he has not seen in three years, were playing in a local softball league when their son got the news he was drafted.
Rincones Jr was always steadfast in his ambitions for a big-league career, and it soon became apparent that playing catch with his father or hitting into a net was not going to cut it. So, at the age of 12, his parents put him on a plane to Venezuela, where he stayed with family as a test to see if he could live away from home.
He next lived with an aunt in Florida and honed his craft at an American high school, where he quickly grew frustrated by how far his development was behind kids who had grown up playing baseball.
“I was very angry and bitter that I wasn’t as good as I wanted to be,” he said. “I knew I could play, I knew I was good enough, I just was not at the time as good as I was in my own head. For the first few years of high school I didn’t talk to anyone, mostly because I was mad at myself.”
But his hard work paid off as he impressed scouts in his final high school season and college baseball followed.
Last year he was drafted by MLB’s San Diego Padres, but well down the list at pick number 580 in the 19th round. It was an opportunity Rincones Jr decided against in the hope of boosting his prospects at Florida Atlantic University, where this season he led the team with 19 home runs and 69 runs batted in (RBI).
Rincones Jr’s next steps are still uncertain. First he has to sign with the team, and he will almost certainly end up in their minor league affiliate system if he does. He is determined to ultimately crack a big-league roster one day.
The news is still settling in for the boy who grew up playing football with his friends at Warout Primary School.
He added: “If I were to put my journey to where I am now on paper and read it to myself, I’d be like, ‘wow.’ You can’t really think about something like that.
“My career is starting now. Everything’s starting now. Now it’s begun, the real work starts.
“I’m very stubborn. You tell me I can’t do something, I guarantee you I’m going to eventually do it.”