Tottenham have never been under pressure to become competitive for the Premier League title. Because it isn't a realistic goal for them considering their history so far. But if you are playing for a team like Bayern Munich you had better do your best to win and be praised by people.
Now, we need to see how good is Harry Kane playing under pressure. He was good in Tottenham when playing without pressure, I hope it will be same. However do Southgate is pressuring Kane when he play for England? Kane is still good when he play for England.
Qualified for UCL has been also the minimum target that may be planned by the club. The players have responsibility to achieve it as the club has paid them to do their jobs. I never think kane played in totenham without pressure.
The pressure is something that will be motivating the player to work even harder to achieve what has already become its target.