Here's the breakdown so far:
1. In the high school, MC loves Sakura. Sakura loves Kurahashi. Kurahashi is meh. At some point, Kurahashi probably think, "why not". Either he really likes Sakura or just wants an easy night with her, regardless, that's the first "NTR" in the story. MC sees that and interrupts them. Sakura hates MC for this (well, at least emotion explosion; she may not really mean it indicated later). She curses MC, wishing if he weren't to exist in the first place. Then, she time leaps into the future, about 16 years duration of time.
2. If she leaps into the future, and only she alone, then the world as of now loses her. That's why the whole school is confused. Some even suspect MC does something wrong with her because MC is last seen with her. Kurahashi has his doubts and tails MC as MC goes to Sakura's house alone for the first time and introduces himself to Sakura's grandmother. Kurahashi confronts MC here, and most likely starts becoming friends moving forward.
3. Her existence is fragile in this world. She randomly leaps time. This is just a theory, but she may have increased chance of leaping time (future or past) as her feelings become very unstable. Regardless, she has leaped several times by now. First, she leaps 16 years into the future. Then, she leaps several years back. Here, she meets with MC who's now enrolled in a university. MC is unable to cope and move on. He meets a girl who resembles Sakura physically. MC dates her. She finds out about MC's true motivation. She finds out that she's only a temporary. Therefore, she intends to inflict the most pain to the true girl MC actually like. At some point, she meets this true girl, being Sakura. She probably recognizes her immediately since she herself looks exactly like her. She connects the dots, and thus why she forces herself on to MC and have sex right before Sakura's eyes.
4. That incident probably shakes Sakura intensely that she leaps into the future again. Not sure how many years, but the timeframe seems close enough to the first jump (i.e., if they're in year 2000 during high school and leaps into 2016, then now might be year 2015). My prediction is that this jump is slightly to the past before the first jump. Otherwise, MC's reaction won't be full of disbelief.