FWIW, I wouldn't classify Newcomb's Problem as having to do with "consequences in the past" or Counterfactual Mugging as having to do with "consequences in another possible world".

For me, "consequences" refers to the basic cause-and-effect relationship - and consequences always take place downstream.

Anticipating something doesn't really mean that the future is causally affecting the past. If you deconstruct anticipation, it is all actually based on current and previous knowledge.