The Pochettino case was similar to Roberto Di Matteo's, but Roberto Di Matteo ended up winning the Premier League title for Chelsea. When Roberto Di Matteo became Chelsea's head coach, he lost a lot of matches with Chelsea at the beginning of the Premier League, but all of a sudden Roberto Di Matteo found a tactic that worked for him at Chelsea in the middle of the Premier League season, and he won the Premier League title that year.
I agree to your comparison but there is not accurate point. Di Matteo did not win any Premier League title with Chelsea, what he won with them is Champions League and it is a first Champions League title in Chelsea history.
Roberto Di Matteo's managerial careerOn 19 May 2012, Di Matteo guided Chelsea to victory in the 2012 UEFA Champions League Final, defeating Bayern Munich at the Allianz Arena. The match had ended 1–1 after extra time with Chelsea coming out victorious in the penalty shootout.[45] This was Chelsea's first Champions League title, and qualified them for the 2012–13 Champions League, in place of London rivals Tottenham Hotspur.[46] With this win Chelsea also became the first London club to win the Champions League.[47]
I believe this decision to end the contract with Pochettino is worse than their decision on Di Matteo years ago. Because Pochettino is a more experienced coach than Di Matteo and he has potential to improve Chelsea performances more in a next season. With Di Matteo, his Champions League title does not mean too much about his managerial ability and he can fail in later seasons that we witnessed. After that title, his career falls down a lot, sacked by Chelsea, and did not achieve good results with other clubs.