So, Timeline Variance is a Thing, it has an energy signature and can be traced. And we've seen what the temporal reset charges do - they nuke the entire area, but selectively. One would presume that they do so by only targeting people and objects which have a variance signature.
In which case, why does The Variant dropping them off in loads of different times and places cause divergent timelines? If a charge goes off where there's nothing variant to be erased, wouldn't it be just a momentary harmless light show? Maybe The Variant changed their targeting parameters.