Presumably, what Hanyuu is doing every time the world resets is not actually moving everybody through time, but into a place on an adjacent dimension equivalent to a few weeks in the past of the original dimension.
Because each dimension has collapsed from a quantum state with slightly different initial conditions, with infinite possible variety, causal determinism can cause certain events to play out completely differently than they would have in a separate dimension.
Ultimately, in all of the dimensions we see in the series, it is Takano who is behind it all, but sometimes she is manipulating people directly and sometimes things just happen to play their course in a bad way.
I mean, hey, who do you think they got the syringes from? They may have been casually left out in the open in the clinic... or handed to them directly.
And let's not forget her notes.