The Spurs boss approached Tel on the pitch at full-time and appeared to give the forward a dressing down, with Tel having struggled to make an impact after coming on as a makeshift striker.
The moment fuelled speculation of a rift between the pair, with some observers online even suggesting Tel had responded by telling his manager: "I was here to play football."
However, lip reader Nicola Hickling, founder of LipReader, has offered a different account of the exchange. According to Hickling, speaking to the Daily Mail, De Zerbi told Tel: "You're playing like a stud," appearing to suggest the forward was running around aimlessly.
De Zerbi is then seen spinning, as if demonstrating a striker's movement, adding: "Like that. I need like that, attack focus," according to Hickling's reading. Tel is said to have replied: "Yeah, but then I went back to play for the ball."
De Zerbi later gave his own account of the conversation in his post-match press conference, explaining he had been coaching Tel on positioning.
"Yes, I coached him on the pitch," De Zerbi said. "The body shape of a striker. The striker can play with the shoulder on the goal. If we are playing with Maddison, Kudus and Savio, he has to play as a striker, and the striker has to look at the goal, no? Or on the cross of Robertson. He has to stay inside because he started his career as a striker. Now he's playing as a winger, but he started in his career as a striker."
Tel had been dropped to the bench for the Everton match after De Zerbi publicly criticised his performance against Nottingham Forest the previous week, but the Italian insisted there was no issue between the pair.
"But I love Mathys as a player, as a guy. There is not a problem," he added.
Tottenham are next in action on Tuesday when they travel to Liverpool in the Carabao Cup third round, before hosting Aston Villa on Saturday.