What does it mean to 'advert' to the factors of jhana after emerging from jhana?
In this context "advert" would mean to recall a cue that produces the desired effect.

For example in second jhana, to produce rapture and happiness without the use of applied/sustained thought, one may turn attention to the muscles of the face, temples, neck, shoulders, diaphragm, chest -- and recall the sensations they experience when feeling happy and joyful.

In first jhana, it would be recalling a particular idea (e.g. the happy fact that one is now separated from unskillful mental qualities due to having realized the Path).

P.S. I would not take "after emerging" literally. "After emerging" aka "post-meditation" generally means one's day-to-day practice outside of formal meditation.