I've been looking for information forever in regards to what happens when, how long it takes to do phase 1, 2, etc. I think I caught my first glimpse of it today in the Anime during a re-watch.
At the begining of the series, both Anime and Manga, Minato is looking at the results of the entrance examination posted at Tokyo University.
This tells us two things. He's already attempted, and its already posted. If we check the Tokyo Universities website, we find out quickly that one round of entrance exams happen Jan-March of the year, with the results being announced between February and April of the same year. We also know "The blooming of the cherry blossoms varies each year but it usually starts in late March and lasts for about one month." from blog.gaijinpot.com/significance-of-the-cherry-blossoms-in-japan. So this would confirm late march, early april where Minato discovered he didnt get in, and informs his mother. Its this same day he meets Musubi, and has her winged 'within the week' if not the next day.
Now, at the end of the first season, Tsukuimi and others are seeing Minato off. "I don't know why you insist on..." being stated by the erstwhile water sekirei while their Ashikabi departs to "WRITE THE ENTRANCE EXAM". We already know Minato's shown no interest in OTHER schools since he'd failed at least twice to get in. This is his third try.
We also know that its not nescessarily been two years, just 1 year as Tokyo U allows it to be written twice a year. At least according to their website.
So from all this, I suppose we can presume that the first season (and the similar chapters in the books) takes place from mid-late march, until the 2nd entrance exams. A quick look at Todai's website... give the impression at least that written and ORAL exams for entrance, take place last week or two of August. Assuming its not Medicine (which is later, May/june/july & Sept/Oct/Nov vs other tracts)
So either (and this is believable) Minato is trying for medicine (I recall somewhere it saying 'the second blossoming' which would be later in the period, like the autumn summer), meaning summer is nearly coming to an end by the time the first season is done. 1-4 months max. It takes about 2 months to write the exams and get the results (again I'm guessing).
If anyone here knows my assumptions above to be wrongly presumed, let me know. I love to pick apart timelines like this to get a better gauge on how long Minato has to REALLY change and man up to help his sekirei survive.
We also know Miya Asama, leaves to visit Takehito's grave site at least twice if not three times that is MENTIONED over the course of the manga where Season 2 would have hypothetically ended (Before the boat SS Minaka). In fact, even before the Jinki's are being given as prizes.
Point - Karasuba visits Musubi and scares the crap out of Matsu in the first season. Where is Miya? Visiting her deceased husband's grave.
Point - Higa's sekirei attack Maison Izumo in the second season when Matsu, Ku and the others are trying to rescue Uzume's Ashikabi from Higa's control. Where is Miya? Visiting her deceased husband's grave.
We know at last TWO months have passed by the time season 2 ends. The first Jinki hasn't even been awarded yet. Hell its just after Kagari gets winged when the 'award' for the first jinki is hinted at for stopping Minato's group from entering MBI Tower.
So, 3-4 months isn't really that long to try to wrap your head around this small group being suddenly 'yours', while trying to understand an insane game.