They were just reading straight from a transit or total station. No need to establish a basis of bearings.
If you pick up surveying books from the black transit days it's very common.
Deflections are what the name implies; a deviation from the direction you are currently traveling. If you are heading east and deflect 45 left, you will be heading northeast. If you are heading east and deflect 45 right, you will be heading southeast. Pretty simple stuff...
Any time we used deflection angles it was in relation to the foresight (left or right) Also made it easy to compute offsets to the line you were running.
This has always been a deflection angle in civil
One advantage of deflection angles is when the traverse lines are to be connected by curves, the deflection angle is equal to the delta, or central angle, of the curve. That solves some of the problems where surveyors make the most mistakes: adding and subtracting.