Considering that Loki hasn't even tried to use his magic for any defense or offense at this point....my thought (read: hope) is that Loki is playing possum, showcasing how "weak" he is to the other one so they will underestimate him and reveal more than they intend. Because otherwise....this isn't a fraction of the Loki we have seen in other outings.
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.
"Cooper has appeared in the story lines of the television series Prison Break, The Blacklist, NewsRadio, Leverage, Journeyman, Renegade, Numb3rs, 30 Rock, Drunk History, and Loki, as well as the 1981 film The Pursuit of D. B. Cooper, the 2004 film Without a Paddle, and a book titled The Vesuvius Prophecy, based on The 4400 TV series."
If it is isolated, it is then... outside the normal timestream! I don't care about what hand-waving they to around how it is made separate - indeed, I don't think they'll address it at all unless it becomes plot-relevant.