@Oeconomist it was aborted though? i mean your whole previous argument is about how they could have still blown it up and by they i mean his teammate.
The real question is why would he abort the mission just based on police presence around building, i mean you saw how amicably he went into police custody because he has no harmful evidence on his person so even if he was caught walking around in an area where he shouldn't be its not like they could pin anything on him. If he knew that the main character could somehow deep dive into the memories of a comatose survivor of a shipwreck maybe he would abort the mission before he went there but you really can't plan for that.
The other burning question is how the teammate got in / out of the boundaries without alerting one of the 5 people who can see spirits.
We can assume that it wasn't police officer because otherwise it would have been stopped at a much earlier stage like you mentioned plus chibi detective would have seen spirit around the precinct and could tell who was spying with it.
Our next best bet and my running theory is that one of the shinto priests performing an exorcism is fake, which seems pretty plausible seeing as this most recently vengeful spirit was killed at a shinto shrine which could have been taken over by the organization for this op.
Again for clarity sake to address your first point again. Police presences means literally nothing to them and the ghosts as shown by the fact that one managed to waltz into a prison cell and blow him up, so why would they need to abort it unless they somehow acquired the information that the target has been moved ahead of time.