Frank, who joined Spurs from fellow Premier League side Brentford, has made an immediate impact in north London. Following a 3-0 win over Burnley on the opening day, Spurs delivered another complete performance to sit top of the Premier League table, boasting back-to-back clean sheets.
First-half goals from Johnson and Palhinha sealed the win at the Etihad. Johnson opened the scoring by finishing a well-worked move set up by Richarlison, while Palhinha capitalized on a goalkeeping error from City's James Trafford to double the lead.
The win also served as a redemption of sorts, after Spurs had squandered a 2-0 lead against Paris Saint-Germain in the UEFA Super Cup earlier this month, eventually losing on penalties. This time, however, there was no collapse - just a disciplined, tactical masterclass from Frank's well-organized side.
Speaking after the match, Johnson highlighted the differences between Frank and former manager Ange Postecoglou. "Nothing massively, they're just two different coaches," he told TNT Sports. "I'm really enjoying it. A lot of detail goes into set-pieces, but at the same time, he gives us attacking freedom.
"The clean sheets have been big too - keeping two already, and one of them against Man City, which is never easy. I've played here a lot and usually concede goals."
Johnson has now scored in both of Spurs' Premier League games this season, continuing his strong form after netting the winning goal in the Europa League final last May.
Palhinha, who joined Tottenham on a season-long loan from Bayern Munich, also credited Frank as a major reason for his move back to the Premier League.
"First of all, it was the coach," Palhinha said. "He really pushed for me to come here and showed me the project at Tottenham. It's a great club, and I'm really happy to be back in the Premier League. I'm happy, my family is happy, and now I want to enjoy this top club and top atmosphere again."
Although Spurs missed out on signing Eberechi Eze, who opted to join Arsenal, Frank has brought in Palhinha and Mohamed Kudus - both of whom have already played important roles in theirs strong start.
Tottenham will return home to face Bournemouth in their final Premier League match before the international break. The club will also learn their Champions League group-stage opponents on Thursday.