In the few comments and little bit of fandom I've been able to find, I see a lot of hate for "the traitor." And... I feel like that's terribly unfair.
I love how they took precautions. "No one with family." No one outside of the... clan, if you will, of power-users. No loose ends or open holes for someone to get hurt or used. Shun planned ahead.
Remember, this school only happened once. Shun only had one chance, because he didn't think of it until his next to last time leap. The entirety of the school's history has been during Shun's final time leap, when he went blind. So he, and Kumagami, and whoever else is part of the decision-making team, decided, "none of the adults can have family." Kind of like Jedi, you know? Nothing that could be used against them, nothing that could make them give in through fear.
Somehow, Furuki slipped through the cracks.
He looks awfully young to me. Probably had just been born when it happened, and he just has his hair dyed.
In any case, he wanted to help more power-users. His motives for joining are not all that different from Shun's reason for founding the school- to save lives. Similarly, Furuki's motive for betraying them is no different than Shun's ultimate goal- to save his family.
Personally, I feel like the only thing Furuki should be blamed for was lying and saying he had no family. But even at that, it was for a good reason.
And on top of this, neither Shun nor Kumagami blamed him.
(Kumagami speaking here.)
Shun doesn't blame Furuki even when Kumagami's life is in danger. He blames himself.
Not entirely certain whether he knew Furuki had a family before this or not. In any case, Shun takes responsibility. Either he did know, and let him stay, or he didn't know because he didn't do enough research. Either way, it was his responsibility.