The cooling break ought to have been a moment of opportunity for Milan, a chance to come together and plan a final assault. They had just pulled level at 2-2 away to Lazio, Rafael Leão driving the ball home from Tammy Abraham’s pass barely a minute after they were both introduced from the bench.

With a little over a quarter of an hour remaining, players gathered around their manager, Paulo Fonseca, to take on water and listen to his instructions. All except for Leão and Theo Hernández, who convened instead on the far side of the pitch.

We would later be told this was a non-incident. Hernández, introduced as part of the same quadruple substitution that sent on Leão and Abraham, and likewise involved in Milan’s equaliser, said: “We had been on for two minutes, we didn’t need a cooling break. It was nothing against the team or the manager.” Fonseca backed that version of events, adding: “We don’t need to make problems where there aren’t any.”

Yet Hernández’s explanation was undermined by the fact he had still used the pause to walk to the far side of the pitch and get a drink. The former Milan captain, Massimo Ambrosini, spoke for a sceptical audience during his analysis for Dazn, describing the scene as “not beautiful” and “the outward sign of some unease, something you don’t want to have to see or justify.”

Fonseca’s decision to omit Leão and Hernández from his starting XI had been a bold one. The Portuguese player is Milan’s best-paid and biggest star, a man who delivered 15 goals and 14 assists last season from the left-wing. Hernández is his perfect foil, the adventuring full-back whose runs from deep create overloads and make space for both to exploit. The Frenchman had 16 goal contributions of his own in 2023-24.

Each of them, though, had underperformed as Milan began this campaign with a 2-2 draw at home against Torino and a loss away to promoted Parma. Hernández was at fault on both goals the Rossoneri conceded in the latter game, the left-back allowing opponents to get in behind him on each occasion.

Post-game analysis by the Italian broadcaster Sky Sport highlighted his apparent lack of energy. Hernández was seen tracking back at 21km/h (13mph) and 17km/h (10.6mph) on Parma’s goals, both times about 9km/h (5.6mph) slower than the players he should have been marking. Unacceptable numbers for one of the fastest defenders on the continent, clocked at a top speed of 35.7km/h (22.2mph) during Euro 2024.

Still, Fonseca insisted his decision to drop Hernández and Leão from the starting line-up against Lazio was not a punishment. “It’s just a choice for this game,” he said before kickoff. “Theo is not physically at his best right now. I spoke to them both and they understood this choice is about the moment that the team and the players are going through.”

Hired to replace Stefano Pioli this summer, Fonseca was navigating choppy waters from the start. A vocal section of Milan’s fanbase had wanted a change of manager for some time, frustrated at how their team fell backwards after winning Serie A in 2022. Yet when the club finally acquiesced, with Pioli departing at the end of last season, those same supporters appeared underwhelmed by the alternatives.

Reports the club were close to hiring Julen Lopetegui in May were met with open protest, Ultras calling a silent “strike” at their next home game. Fonseca was a compromise candidate, someone whose success steering Lille into the Champions League was respected and who had worked in Italy before – a significant consideration in a country that can still retain an insular mindset about coaching.

Still, he was not the proven winner many fans hoped for. After watching Internazionale move ahead of them by claiming their 20th Scudetto last season, Milan’s supporters wanted to strike back immediately. Fonseca did start to win them over during a pre-season tour of America in which they beat Manchester City, Real Madrid and Barcelona.

Asked about his objectives, the former Roma manager replied with an unambiguous, “to win the Scudetto.” Sweet music to fans’ ears, interrupted abruptly by seeing their team fall 2-0 behind in their opener against Torino. Although summer signing Álvaro Morata inspired a late rally to draw that game, the outlook has not improved much since.

Losing to Parma was a humiliation, and Saturday’s game against Lazio was almost another. Milan made an encouraging start, taking an early lead with Strahinja Pavlovic’s header from a corner and largely controlling the first half. But the ease with which they collapsed after the interval, conceding twice in five minutes, was shocking.

Most galling of all, Valentín Castellanos and Boulaye Dia’s goals looked identical to the previous four Milan have conceded under Fonseca. Every single one has resulted from an opponent attacking down the left and crossing for a teammate to convert at the back post. Hernández, as poor as he was against Parma, has only been on the pitch for half of them.

Fixing the defence was a priority for whoever replaced Pioli. Despite finishing second last season, Milan conceded 49 goals in 38 games. Pavlovic, a Serbia international, was added at centre-back, and Emerson Royal arrived as an alternative to Davide Calabria – whose performances have dropped off badly in the last year – on the right. The defensive midfielder Youssouf Fofana was signed from Monaco.

It is too soon to judge these players, who have started four Serie A games between them. New signings have had an encouraging impact at the other end of the pitch. Abraham, who completed his loan move from Roma on Friday, set up Leão with only his third touch in a Milan shirt. Morata scored within 30 minutes of making his debut, though he has been out injured since.

The hope for Milan is that improvement might be achieved not just through new signings but year-two improvements from players who joined last season – the likes of Samuel Chukwueze, Tijjani Reijnders and Yunus Musah. Milan have spent close to €200m over the last three transfer windows. Results this season will reflect the work of directors Giorgio Furlani and Geoffrey Moncada, too, as well as Zlatan Ibrahimovic, who returned in December as a senior adviser to the RedBird ownership group.

It is the manager, though, who remains first in the line of fire. Three games into his tenure, Fonseca is already having to contend with newspaper reports his position is under threat and that he could be replaced by Massimiliano Allegri. How real those claims are is a matter of conjecture, but Rudi Garcia’s sacking after 16 games with Napoli last season offers a recent reminder of how quickly relationships can sour.

One way or another, Milan fans will be impatient to see improvement after the international break. A daunting demand, given that the team’s next three games include a Champions League visit from Liverpool and this season’s first derby against Inter.

All of which will only be more complicated to navigate if Fonseca does indeed lack the support of senior players like Leão and Hernández. Perhaps there is truly no animosity behind the scenes, and a cooling break is just a cooling break after all. But it was not just the over-30C temperatures in Rome on Saturday night causing Fonseca to sweat.