This idea was definitely a little confusing to get---but another method of thinking about this that is helpful for me is treating the "A unless/or/until/without B" statement as an "either A or B" statement. For example, "Blackouts will occur unless the heat wave abates" can be rephrased as "Either blackouts occur, or the heat wave abates." That way, it feels more intuitive to presume that:

If not A, then B. (If blackouts don't occur, then the heat wave abates)

If not B, then A. (If the heat wave doesn't abate, then blackouts will occur)

This is just what has helped me so far--if there's something wrong with this reasoning, let me know!