Opinions in football can shift so dramatically from one day to the next that it is easy to forget the disbelief and anger that greeted Southampton's decision to replace Nigel Adkins with Mauricio Pochettino in January. Here, it was said, was just another tiresome example of the impatience and disloyalty of those who run clubs these days.

Adkins had taken Southampton from League One to the Premier League in the space of two years, and two days before he was sacked his side drew 2-2 with Chelsea at Stamford Bridge after finding themselves 2-0 down at half-time. There's gratitude for you.

However Nicola Cortese, the executive chairman, was undeterred. Out went Adkins and in came Pochettino, an inexperienced Argentinian who spoke no English. It seemed like a recipe for disaster, as if Southampton, who were three points above the bottom three, were trying to get relegated.

Nine months later how foolish those predictions look. There have been victories over Chelsea, Liverpool and Manchester City, and Southampton visit Manchester United on Saturday afternoon with many tipping them to win at Old Trafford for the first time since 1988. Southampton are fourth, two points off the top and four above United. Given that United lost their last home match 2-1 to West Bromwich Albion, this is a tremendous opportunity for Saints to put one over on David Moyes.

It is not Pochettino's style to get carried away – especially not in October. Although three successive wins, including the 1-0 victory at Liverpool last month, have lifted Southampton into Champions League places, the 41-year-old refuses to be drawn into making bombastic predictions he might regret.

Instead he speaks extensively about the need for his players to deal with the fact that opponents are starting to view them in a different light.

Perhaps such poise is reflected in the measured way Southampton play. When Adkins was in charge they attacked thrillingly but were fragile in defence and Pochettino has been able to strike a greater balance. This season, Southampton have conceded two goals in seven matches and Artur Boruc has kept five clean sheets. Only Roma, top of Serie A with one goal conceded, have a better defensive record in Europe's top leagues.

Southampton's solidity can partly be explained by the way Dejan Lovren has excelled in central defence since arriving for £8.5m from Lyon in the summer but also by the way Southampton mimic Barcelona by pressing high up the pitch in order to win the ball back as quickly as possible. When Southampton lost 2-1 at United in Pochettino's second game last season, Sir Alex Ferguson admitted that the visitors deserved more. "We were fortunate to win the game," Ferguson said. "They pushed on top of us and didn't give us any time on the ball."

Pochettino spent three years as manager of Espanyol in La Liga and the Spanish influence is obvious: you cannot concede if you have the ball and Southampton tend to dominate possession – Victor Wanyama, the £12.5m signing from Celtic, has been an effective shield in front of the defence. Boruc has rarely had to perform heroics, although he was magnificent in the 2-0 win over Swansea City two weeks ago.

"Our set-up is very clear," Pochettino said after the 2-0 win over Crystal Palace last month. "We want to defend, keeping possession of the ball. We want to be as effective on the attack, to be as far away from our side of the pitch as possible. We also know we are running a certain risk when we play that way because we might be giving the ball away, but it is our philosophy. We want to believe that we can succeed playing in that way."

Pochettino does not speak English in press conferences yet, although he clearly understands the questions and has occasionally offered a few words. Maybe, at this point, he is just keeping his interpreter in a job. However he appreciates English football and has made good use of a youth academy that produced Gareth Bale and Theo Walcott. Calum Chambers, Luke Shaw and James Ward-Prowse, three 18-year-olds, have all impressed.

Not everything is perfect. There are times when Southampton have been bogged down against deep defences, the partnership between Daniel Osvaldo and Rickie Lambert is not quite clicking yet, and Gaston Ramírez's agent has voiced his client's displeasure at being left out in recent weeks.

More pertinently, there is also the added pressure of working for Cortese, who made headlines last week by describing the manager's "important" role as "a department head like others" when explaining how the club's "continental" structure works.

It was an unfortunate turn of phrase and meant that on the eve of Southampton's biggest match of the season, Pochettino's unflappable nature was tested by uncomfortable questions about the executive chairman's comments. Cortese is not a man who is shy of making enemies – Matt Le Tissier simply says "he is not a very nice human being" – and Pochettino went on the defensive, unwilling to say anything that might put him at odds with his employer.

At one point, Pochettino fell back on his lack of English, produced his best confused look and made out he did not understand the thrust of a simple question which had to be rephrased four times before it was answered. It made for a slightly tense occasion when there should have been nothing but positivity.

"I would never ever, ever speak about the words of my chairman or the interpretation of the words that are done of my chairman," Pochettino said. "All I can say is that I have an amazing relationship with him. We get along, we speak every day, we have a great relationship. I am in charge of the sports department. I am very happy within that role. We have a very good relationship.

"I don't comment on what the chairman has said. I am the manager. I just try to establish how I want the team to play, our philosophy of how we play football, and that is my role within the team, nothing else."

So, then, does it matter who the manager is? "It's always the manager that sets how the team wants to play," Pochettino said. "Barcelona under [Pep] Guardiola and Barcelona under [Tito] Vilanova and Barcelona under [Tata] Martino play in different ways.

"Southampton don't play the same way as they did under Adkins under Pochettino. It's also clear that the club has a certain philosophy and the club will try to find a manager to try to execute that philosophy in the way that the club wants, so that's why I am here."

And the players enjoy the philosophy. Adam Lallana, the captain, has said that Pochettino may manage one of Europe's big clubs one day. Pochettino, though, was unmoved by the praise. "I'm not one to set myself long-term goals, I only think about the short term," he said. Probably wise.