The Argentine was appointed as the Blues' head coach earlier in the summer following a year-and-a-half stint at Paris Saint-Germain.
It has seen Pochettino return to English football for the first time since 2019 when he was in charge at Spurs, where he spent just over five years.
He oversaw one of the Premier League's most iconic matches as Spurs travelled to Chelsea in 2016 needing a win to keep their title hopes alive against Leicester, but had to settle for a 2-2 draw.
The match saw 12 yellow cards handed out and fiery scenes on the pitch before and after the full-time whistle, with Rose involved in the encounter.
Seven years on, Pochettino's allegiances have flipped and when asked about his appointment at the Blues, Rose said: "For me, never ever would I have ever thought that Mauricio would be the manager of Chelsea.
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"I would say I was hoping and expecting him to go back to Spurs and obviously it didn't materialise.
"For me, obviously I was at Spurs for a long time, 14 years, I never understood the rivalry until that game in 2016. I didn't know Chelsea hated Spurs so much."
The famous clash between the two sides, now dubbed as the 'Battle of the Bridge', was one that saw Spurs go 2-0 up.
However Gary Cahill's goal before the hour mark offered Chelsea hope of a comeback, one that was sealed by Eden Hazard's curling strike with seven minutes left to play.
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It was a crushing defeat for Spurs as tensions boiled over, with Rose adding: "Honestly, going 2-0 up and then after that it just felt like a school football match with everyone just trying to get yellow cards and what not.
"When Hazard came on and absolutely just turned up, obviously we lost it in 45 minutes, it was hard to take."
"It was difficult because that season, Chelsea were poor," he said when asked if it was difficult to keep his head in such a dramatic match.
"Jose Mourinho had lost his job and Guus Hiddink came in, they were poor, they were mid-table. I remember hearing that that week leading up to the game, it was the best they've ever trained.
"It was difficult, I think I came off after about 75/80 minutes, had I still been on the pitch towards the end when it was really kicking-off, there was a good chance I would have been sent off!"
Pochettino picked up his second win as Chelsea boss on Wednesday night as they beat AFC Wimbledon 2-1 in the Carabao Cup.