The hell did the clock keepers even do
From my understanding, they went back in time causing a change (or multiple?) that had a butterfly (or combined) effect leading to this current timeline.
I think the effects shown so far are
- Mitsuba is still alive
- Hanako doesn't exist
- Amane is still alive or at least lived longer
- In return Tsukasa is much more aggressive/violent
- No other supernaturals have shown so far
- Aoi and Akane's romance is twisted, since Teru is engaged(?) with Aoi. This is related to her being a shrine maiden descendant/supernatural stuff iirc
So my takeaway from this is that they prevented Amane from killing (the possessed) Tsukasa - and thus the events unfolding afterwards - (assuming that even happened) meaning both lived longer, but in return the thing possessing Tsukasa grew much stronger & there's no Hanako to keep it in check.
Maybe, the possessed Tsukasa went then on to slaughter other supernaturals at school. In any case, this strong supernatural probably caused changes to overall supernatural landscape, leading to heightened tensions and thus the engagement of Teru and Aoi to strengthen the exorcists.
As for why Mitsuba's alive due to this change, either
a) there was more to his death then a simple traffic accident so it was affected by the change or (my guess)
b) since the probability to die in a traffic accident is rather low, this alternative timeline is simply one where he didn't get unlucky (e.g. went another route and or at a slightly different time...).
Additionally, it could be possibly that the clock keepers made many small changes (as mentioned above), although I doubt they'd change the fate of individual students when their aim is to resolve the crisis with the supernaturals.
sorry for the rant