It's the detailed scene on how Tatsuya came to save Miyuki cs, when they were exposed to cast-jamming. The effect cast-jamming was really tough to Minami because of the noise, seeing Minami was in pain, Miyuki almost lost control because that reminded her about Honami in Okinawa.
Minami calmed down Miyuki by saying she's fine, and reminded her Tatsuya's order to Miyuki should refrain of using magic when the opponents are non-magicians due to her position as next leader of Yotsuba. Tatsuya said to Miyuki to rely on Minami as possible when he rushing to rescue. (This is from volume 18 though) Miyuki then calmed down, and made an encirclement of psion cloud which acted as cushion to reduce the effects of cast-jamming's noise.
And then Tatsuya came the scene. This scene is about Tatsuya playing with Humanist and on how he disabled 5 people in 3 seconds. Cameras caught everything that happen. Tatsuya even did say to Humanist to cease the confrontation and pointing to the camera that all proofs are there.
Tatsuya said this for his alibi. In his defence, he will be able to say his act was a proper self-defense. He disabled all Humanist purely with physical combat skill. No magic invoked and there's Fujibayashi in case of emergency. She will be able to remove any trace of magic that Tatsuya used just like she always did
Last paragraph, the humanist that lost the will to fight suddenly under control of spirit magic, and Tatsuya immediately disable that magic using gram demolition.
By A Wikia contributor 113.163.124.102
That scene Tatsuya and Miyuki is in swimming pool, Tatsuya tried to soothe her, telling her everything will be okay, Miyuki's being nervous after she and her friends got attacked by a humanist group last volume, she was feared that Minami would end up like Honami and it brings back bad memory.
Credit TA
After the humanist leader lost consciousness, he stood up again while raising both of his arms forward. On his hands, there are spiritual beings (SB), which is also called as element. But, it has an ominous purple flame, so Tatsuya thinks, "evil spirit"(邪靈) may be better name than "element".
The humanist leader had two weapons: Stun Whip and a handgun. A handgun is illegal, and a stun whip can only be gotten from a police or a supplier who supplies weapons to police force.
Once, Tatsuya has a visual contact with a person, Tatsuya can track him or her. But, if Tatsuya uses this power, Tatsuya has to stop monitoring Miyuki and concentrate on Gu Jie. Tatsuya thinks, Gu Jie is not worth enough for Tatsuya to stop watching over Miyuki.
Tatsuya can look into past for 24 hours prior to the present time (the time when he uses his eye to look into the past.)
Tatsuya cannot foresee the future. In this event, Tatsuya had a gut feeling that Miyuki may be in danger, and he was right.