Pep touches down in a league, dominates, and develops some of that country's best players into optimal technicians and decision-makers. Soon enough, other teams in the league mimic his coaching and playing styles, which trickles down to the national team, thus increasing their performance. It seems like a reach, but it isn't- the evidence tells us this is the case, especially in countries like Spain, Germany, and England, where most of the national team plays in their domestic league.
The first example: 2008, when Barcelona tasked Guardiola with managing a team falling well below expectations. He guides the club to their first-ever treble in his debut season, and by 2010 when the Spanish National team wins its first-ever World Cup, they do so by starting 6 of his Barcelona players in the final. A few years later, for the 2012 Euro Finals win, 5 of the starters are members of his Barcelona team, with a sixth coming off the bench.
He heads over to Bayern Munich in 2013, the club most important to a German National team that hasn't reached a major final for 23 years. A year later, fueled by 6 Bayern Munich players in their starting lineup and a seventh coming off the bench, Germany wins its first World Cup since 1990.
Next, we have Manchester City in 2016, a club that quickly stands at the center of England's National team resurgence. Fast forward to 2018, and England plays in its first World Cup semifinal since 1990. A few years after, they are in the European final, their first major international final in 55 years.
I believe the reason we see this correlation is two-fold.
1. Pep Guardiola's specific coaching style
2. The impact his presence has on the rest of the league.
In that first part, Pep's coaching style is not necessarily the playing style he promotes but rather how he trains his players to interpret the game. When you look beyond the playing out of the back, the tight combinations, and heavy ball domination, the core of Pep Guardiola's coaching philosophy is optimizing his players to make the best possible decision in every scenario.
He develops players who understand, see, and play the game in a manner that generates the most scoring opportunities, which means they rarely make the wrong decision on the ball. That kind of coaching turns average players into good ones, good ones into great ones, and great players into world-class talents. More importantly, it is also that training that influxes a country's national team with Guardiola-trained players who are masters at making the right decision in any given scenario, which makes that slight marginal difference you need for success at the international level.