I recommend that you read it again so you can understand it better.
I already did, my guess is he's another Reincarnation of the people the king know.
They are not necessarily reincarnations. This is most likely an alternate reality, rather than the "future" of Jun's world, which would also explain all the interconnections being maintained as well. Meaning that they are more likely alternate versions. So for all we know, there is also an alternate version of Jun walking around somewhere. That is my personal opinion at least.
Either way though, he is either, as you said, a reincarnation of the third prince, or as I said, an alternate version of the third prince. But seeing as all the reincarnations/alternates have the same personality as the "originals" back in Jun's world, I would not trust Jin's alternate as far I could throw him. Nor do I like or trust the Chief. I think Shiwoo would be better off quitting his job and finding a new one. And this is not based on the Prime Minister's actions, but solely on the way he was talking down to and treating Shiwoo when he called him in for the news. That whole scene just left a bad taste in my mouth.
i need to say yes in this one he looked really coldley yes and the type of tone you can't say no in this matter :o was like shit...what's going on here? :o
yeas I agree he should find another job, but I doubt he quit his job that fast. it going to get even angst XD and yeas I guess it can also be alternate version of the third prince.
maybe yes i was thinking the same plus it makes more sense when he aproge him when he was talking on the whit jun that was really weird so...
that's it?? damn Σ(っ°Д °;)っ so is this new guy is a prince or just a Reincarnation????