Eyebrows may have been raised when Ronald Koeman went to Aston Villa for his first outfield signing of the summer, activating a £7.1m release clause in Idrissa Gueye’s contract and signing the defensive midfielder on a four-year deal.

Villa slipped out of the Premier League last season with a pitiful 17 points and the Senegal international had featured in 35 of those games, his appearance at Everton in November’s 4-0 defeat even seeing him suffer the indignity of being substituted at half-time.

In the 1-1 draw against Tottenham Hotspur on Saturday he lined up for his debut in his usual central midfield berth alongside Gareth Barry, with the previous occupier of that position, James McCarthy, shunted out to a right wing-back position in a fluid 3‑4‑2‑1. By the end of it Gueye had played a key role in securing a point against Champions League-qualified opponents who were basically at full strength and in the process had won over any waverers.

At 5ft 7in and 10st, Gueye has a build similar to N’Golo Kanté, the heartbeat of Leicester City’s title-winning side, and he played a similarly key role in breaking down Spurs’ forays into Everton territory, getting a toe in here, a tackle or an interception there, and playing the ball simply to a team-mate on almost all of the 59 occasions he was on the ball.

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By the end of the game, in which Everton started brightly and Gerard Deulofeu missed a golden chance in first-half injury time to add to Ross Barkley’s opener, Everton were hanging on grimly with the substitute Arouna Koné up front and their goal threat all but gone. Érik Lamela had equalised with a header after he got goalside of another debutant, Mason Holgate, but the third new boy, the goalkeeper Maarten Stekelenburg, produced a couple of fine saves thereafter as the home crowd grew as jittery as it ever was in the Roberto Martínez years.

“Idrissa’s the kind of player that puts a lot of energy [into his game], he’s aggressive and he wins second balls,” Koeman said. “He can play good football. With Gareth and the second balls of Idrissa, that makes the team strong. The cleverness on the ball in midfield comes from Gareth but one of Idrissa’s qualities is to put that energy into the team, to win second balls and to press at the right moment.”

The manager was less pleased with the stamina of many of the players he inherited, who last week he warned had only about 70% of the fitness level he is seeking for the season ahead. Despite being happy enough with a point in his first game when he was forced to start with the winger Deulofeu in a central attacking position with Romelu Lukaku sitting in the stand, apparently with a heel injury, he returned to the theme. “It was good for Gerard against Tottenham because they like to play with a high line defensively and there’s a lot of space,” Koeman said.

“You saw the big opportunity before half-time. He pressed really good, there was no other option for the full‑back but to play the ball back to the goalkeeper and he was between them. He needs to score, but it’s still not for 90 minutes [that he can be effective]. Gerard, like Kevin [Mirallas], I like the players, but they need to do more. They need to run more, they need to press more. That’s all about workrate. We will work on it. Gerard needs to take more responsibility for the team and to do all the jobs, also defending. That makes the team stronger.”

The Dutchman said he already has a reaction from Barkley, who was still working hard for the team in the second half, but Deulofeu and Mirallas were substituted after the Spurs equaliser, and the 35-year-old Barry joined them with five minutes remaining and the Everton backline getting deeper.

Throughout it all Gueye remained steadfast as Tottenham camped around the Everton goal area, chipping away at their attacking moves, breaking up the play and relieving pressure. And as an added joy for traditionalists, he was the only player wearing black boots.