I don't like Pochettino's coaching style. He likes buying already-established players. I will not be wrong if I assume that he depends on big names to win trophies. I am more comfortable with coaches that build young players. Coaches that groom unknown players to superstars are the best in the world.
Pochettino is a great coach who loves to play pure attacking football, he of course didn't win any trophies in Tottenham, neither did the club have the money to buy "already eatablished players" like you say, Pochettino did so well to play good football with the players at his disposal when he was in Spurs.
Having said that, Poch won trophies in PSG and that's all the trophies that he has won, mind you that most of the transfers that take place in PSG is done solely by the club, without even the managers consent, and that's the same thing happening in Chelsea now, Todd Boehly is just buying players left, right and center, none of them have been players that the manager identified himself. Chelsea are doing crazy business right now, hiring too many players, many of which they don't even need.