They're one of the most active teams in the transfer window and have spent over £452 already so it's pretty clear that they're splashing money to improve the quality of the team. Of course this is done for the benefit of the fans too. Most of the support base will probably understand if there's an increase in the price of the ticket or other club merchandise.
It doesn't matter how active Chelsea are in the transfer market and how much money is spent because it is the result and the performance on the pitch that will be judged. Because if a budget of that size does not show significant results, Chelsea will automatically receive a lot of criticism, including a failed coach. There are risks involved in carrying the burden of responsibility for a well-known club in England. Pochettino cannot just rely on his reputation at PSG because the positions and players are very different. at PSG he may be successful but any coach who has more than 3 star players will definitely be successful without having to work hard.
Pochettino was challenged to build Chelsea from scratch after several coaches failed. So the question for Pochettino is whether he is able to complete the task or is he not able to do it but is still forced to do it.