Satoko was already bloodied by the time Ooishi reached the shrine, and the bat was present in Satoko's house, so my guess is this:
- Ooishi strongarmed Satoko into helping him investigate the curse, by threatening to release Teppei.
- He arranged for Satoko to invite Keiichi to his house, to also recruit him as usual.
- While carrying the bat, something went down with Tomitake and Takano that caused him to be injected with the syndrome.
- In a rage, he scrapped his plan and bonked Keiichi (who then hallucinates fighting back against Teppei).
- Then Ooishi goes to the shrine and the massacre happens.