It is no accident that Kane, England's No?9, will travel to France on Monday as one of the most feared strikers at Euro 2016. His rise has been about dedication that borders on obsessive, the fitness and coaching methods of Pochettino and his lieutenants and the group approach to finding new and inventive ways of getting better.
When Pochettino gives his players an afternoon off, Kane will regularly contact the rest of Tottenham's attacking players to organise an hour of extra shooting practice. But the session is not players wildly lashing balls towards an empty net while discussing what they might do later, or filming themselves attempting to pull off outrageous trick shots.
Kane's shooting practice is strictly set to between 100 and 150 balls in the hour and all shots must be taken from inside the box and replicate genuine shooting positions that come up during games. There will generally be six offensive players - Kane, Christian Eriksen, Érik Lamela, Dele Alli, Nacer Chadli and Heung-Min Son - and three goalkeepers from the academy who jump at the chance to test themselves against a group of full internationals.
Kane will often go to Tottenham's impressive Enfield training complex on the day after a game and work through what he felt benefited him from the previous Thursday's training session in the match.
Over the week, Kane will attempt to replicate situations that came up in the last match to learn from what went right and what went wrong, and attempt to make sure he is even better prepared in the next fixture.
Kane's desire to learn and get better long predates Pochettino. He was never among the best three players in any of his age groups. When his representative, Marlon Fleischman, first watched him at under-17 level, all the other agents were talking about Cameron Lancaster, now playing for Louisville City in America, Paul McBride, who was released by Spurs in 2012, and Calum Butcher, now at Burton Albion.
Fleischman noticed that while other players caught the eye with stepovers and tricks, Kane always scored and always got better. He was constantly asking questions of his coaches and trying to self-teach different techniques.
There were never any complaints about dropping down divisions to go out on loan, even at Millwall - despite the reservations of some of the Tottenham coaches and scouts. Fleischman had taken another of his clients, Andros Townsend, on loan to Millwall the previous year and thought it would be the perfect education for Kane. Before finalising the deal, he even took Kane's family to watch a match at the Den to make sure everybody was clear what would be facing him.
Millwall supporters are notoriously unforgiving and would not take kindly to a 'Billy Bigtime' turning up and thinking he was too good for the club. But they quickly realised that would not be the case with Kane, who had prepared himself for the loan by watching every one of Teddy Sheringham's 33 League goals for the Lions in the 1990-91 season.
During his final loan spell, Kane spent time on the Leicester City substitutes' bench, ironically next to his current England team-mate Jamie Vardy. The pair were reminded of the image after both scoring in the comeback victory over Germany in March.
The biggest visible change in Kane over the past two years has been his body composition. Pictures of him before Pochettino's arrival at White Hart Lane show a tall, slim youngster whose arms did not quite fill out the sleeves of his shirt.
After assessing the Tottenham squad they inherited on their arrival at the club from Southampton, Pochettino and his staff went about devising personal programmes for the players and the watchword in Kane's case was "power". They wanted to make Kane into the powerful specimen he is today and through that add an extra couple of yards of pace to give him the ability to explode past a defender's challenge when it mattered.
Rather than making him hit the weights, Kane was put through a number of different physical conditioning activities - the content of which remains a closely guarded secret as Tottenham do not want rivals stealing their ideas.
The results have certainly been spectacular as Kane is now one of the most physically impressive players in the Premier League and Roy Hodgson's England squad. Tottenham will not like to see this in black and white, but he looks every inch like a Real Madrid galáctico.
He became the first Englishman in 16 years to win the Premier League's Golden Boot this season and is the first English player since Alan Shearer in 1997 to score more than 20 League goals in back-to-back seasons.
It is not just his goals and work-rate that Pochettino values. Kane has quickly become one of three dressing-room 'generals', along with captain Hugo Lloris and Jan Vertonghen, and gives the speech in the pre-match huddle. Hodgson is also said to have recognised his leadership skills.
Shearer was the last England player to top the scoring charts at a major tournament, when he hit five goals at Euro 96, and it would be no surprise if Kane takes that title this summer, having already claimed the former Blackburn Rovers striker's one-armed celebration.
The best news for Hodgson may well be that Kane's WhatsApp group will remain open during the tournament for Pochettino to tap out any nuggets of wisdom from the armchair in Barcelona where he will be watching. There is certainly a buzz about England's main man.
