True solar time is a correction
True solar time adjusts clock time by location. It can matter when someone is born near an hour boundary or when the recorded time is far from local solar position.
Not every chart changes
Many charts will keep the same hour pillar after adjustment. The important cases are boundary births, unusual locations and time-zone complications.
The responsible approach
When true solar time may change the chart, treat both possibilities carefully instead of forcing certainty. The best reading acknowledges uncertainty.