Upon re-reading the translation of the game's dialogues, I realize I was making wrong assumptions. Here's my (new) interpretation of how the events of IS really happened:
Immediately after the events of DDC, the tsukumogami that were born by the power of the Miracle Mallet (Raiko and the Tsukumo sisters) and the youkai that became aggressive (WaggySaggy, Banki, Kagerou) regained their senses, and realized Seija had manipulated them all. Someone puts a bounty on the amanojaku's head (I believe it was Shinmyomaru, more on that later), and all the wronged youkai go chase after her with impossible barrages, partly out of revenge, partly for that bounty. Seija, feeling threatened, resorts to using the remaining power of the Miracle Mallet and some cheat items to survive and defeat her attackers.
[SPOILER ALERT: Read at your own risk]
This goes on for a week, while the tales of the amanojaku who cheats her way through spread over, catching the attention of stronger youkai. Eventually, Seija crosses paths with Shinmyomaru, and the inchling tries one last time to convince the amanojaku that the social upheaval from DDC is over, and that she should give up. But being the contrarian she is, Seija refuses, saying that the revolution has just begun. Then Sukuna reveals that she convinced the strongest people in Gensokyo (read: Marisa, Reimu, Sakuya, Byakuren, Toyosatomimi, Yukari, etc.) to take the bounty hunt seriously. But Seija is having none of that, and keeps on fighting waves after waves of impossible danmaku. And the rest is what I said earlier.
That's only my interpretation, though. You're free to take it or rebut it.