I think Chelsea fans will be disappointed if they have high hopes for Pochettino. I don't think Pochettino was very successful with PSG. Chelsea's problem is much the same as PSG's. Chelsea's squad has plenty of star players, but the bond between them is weak. Due to this, the performance of the team is not consistent. Pochettino will definitely need to develop a better match strategy, as well as strengthen the bond between the players. Then maybe Chelsea's performance will be somewhat stable. But I don't think Chelsea will fight for the title next season. A longer period of time is needed to build a squad capable of fighting for the title.
We haven't seen his performance with Chelsea, so we have to see how Chelsea plays under Pochettino. For that I hope not to be a big disappointment for Chelsea fans because next season Chelsea is still in the squad building stage and it will take time after having slumped this season. So one of the important things is to give him full support for the policies he has undertaken in building Chelsea to be stronger by being in the top 4.
Pochettino presence is indeed one of the hopes of Chelsea fans because he is quite familiar with the Premier League situation. So that one of the forms that it needs is signing players for some of the gaps in the weaknesses that exist in the depth of the team.