Chelsea also made a hasty decision in my opinion, especially about selling important players. Mason Mount was one of the most important players for Chelsea in recent seasons, Kai Havertz too, but they sold him to Manchester United and Arsenal instead. Admittedly I was pleased when Manchester United managed to sign Mason Mount, but it was a big loss for Pochettino who was hoping for more good depth to his squad.
Mason Mount lost his position in the last season and with Euro 2024 comes after the end of a new season, he does not want to spend time on bench at Chelsea and lose his position in England squad too. He was informed that he is no longer in plan of Chelsea and Pochettino and eventually a story of 18 years (he joined Chelsea Academy at his sixth) comes to the end.
Kai has a better situation than Mason Mount but he does not satisfy with his chance in Chelsea. In contrast, Chelsea thought they should get more better contribution from Kai. So they came to a separation in agreement for better future of the club and the player.
I will not be completely sure Pochettino will succeed in building Chelsea as quickly as expected, that's because he and some players need adaptation. Next season it is clear that there will be many opportunities for players like Mykhailo Mudryk and several other new players, so of course they need time and adjustments to the strategy from their new coach.
It is a long time since he left Tottenham and Premier League and it is not easy to repeat success from one club to another. In addition, in Tottenham, Pochettino did not win any Premier League with Spurs but it is his main task in Chelsea. If no Premier League, no Champions League after two or three seasons, he will lose his job.