Pochettino has a pretty good history in his work to become a coach like in Tottenham who managed to go to the final match even though he was defeated by Liverpool and the best he could achieve was with PSG won France Cup and the French Super Cup. And today he is with Chelsea, maybe many people will hope for him to contribute to an increase in Chelsea's squad that Chelsea has been very down under Lampard's leadership.
There are many important players who leave Chelsea such as Kai Havertz and Mateo Kovacic and the others, it is a very difficult position that Chelsea has today, truly regretted the new coach comes to fix but many players leave, it is a burden will reconstruct Chelsea by Pochettino, but according to this it takes longer to revitalize and build good emotional relationships with new players who have different characters and potentials.
But if he is good at adapting and recognizing the ability of his students, I think there is no need to take much time to make changes to the squad.
Winning Ligue 1 is not best achievement for Pochettino because all manager always winning Ligue 1 tittle with PSG because there are not compete league, but Pochettino success managed Tottenham Hotspur until final stage in Champion League but difficult when becoming PSG head coach managed well in Champion League. Pochettino is not easy manage well Chelsea this season although have competition with domestic league after failure play in Champion League or Europe League due many important players sell.
I think Pochettino have working hardest how to make Chelsea back to the top fourth standings position exactly he need adapt with some position filled by new players without know how difficult and hardest with Primer League competition. Some mistake made by Chelsea with their recruitment not players know and ever play in Primer League and doesn't need time for adapting.
I think we shouldn't expect to see Pochettino doing some miracle for Chelsea, even if he s a good coach and he knows his work, still, Pochettino started working at Chelsea while the team is not in a good situation and we can't expect more from him.
Even if Pochettino makes Chelsea race at the top of the table this is enough for this team in the next season.
Also since Chelsea sold many players and hired other players, I think this time needs some time in the next season.