I think there definitely will be a transition period of sorts. Since he's been in Germany since the age of 17 and is fluent in German, I think his transition would be more similar to a young German player moving to England than to another Korean player making the same move.
He's also going to be in London, which will help with his transition. There's a larger Korean diaspora, and there are two Korean internationals playing in West London to help with his transition as well.
At both HSV and Leverkusen, he was very close with his teammates as he has a very outgoing personality. If he strikes a good friendship with someone like Harry Kane, who similar in age, he should settle in nicely. I think his English is conversant enough with a heavy Germanic accent, so he should, hopefully, become fluent soon. He also seemed popular with the German media due to his personality and fluency, so I'm curious to see how he settles in that respect in London.
As for playing style, I think the faster pace of the English game suits him. There are some deficiencies in his game that Schmidt's system exposed at Leverkusen. He'll still need to work on those, but with pace being so heavily emphasised in England and with Eriksen creating chances, his weaknesses may actually be disguised better in England. So aside from pace, in terms of strength, he has incredibly thick legs. But I think he'll need to keep developing his upper body a little more, but that is something he needed to work on anyway in Germany.
I'm slightly worried as he hasn't been in great form when I watched him in June for the World Cup qualifiers and during his pre-season. The first match against Hoffenheim wasn't that great either. He seemed nonchalant with his off the ball movements and initiating the early press. At the same time, Pochettino's system is somewhat similar and in many ways, much less demanding than Schmidt's system. So I'm cautiously optimistic.