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Anyway, I found the answer but it is hard to explain without screenshot: When you look in the promotion list at the Bailif's there is an arrow when the promotion makes the worker more efficient. However when clicking on the building every worker that can be promoted has an arrow. The difference is only that there are tiny tiny lines around the arrow indicating that the promotion is also beneficial. But those are impossible to notice for someone wearing glasses...
The two arrows you are referring to are different, one is a simple arrow to indicate that you can use that button to promote the villager while the one that shows the tooltip of "optimising worker efficiency" when hovered over has little fireworks around it.
The arrow with the fireworks around it is the one shown in the promotion mandate list only next to jobs that will benefit from a promotion.
See a screenshot for reference: https://ibb.co/HpXPM7cw
The carpenter has the simple arrow and hovering over it shows no tooltip at all. i.e. they do not benefit in productivity from a promotion.