1. Someone logs an instant in time before DST starts and dutifully includes the offset from UTC to avoid ambiguity.
2. After DST starts, the same person in the same location reviews the logged times by a systematic procedure: a) converting the logged times to UTC according to each time's recorded offset and b) converting the UTC time to local time using the current DST offset.
Presto! A time that was frozen in history a month ago has now "changed". "I don't remember doing that during my lunch hour..."