I think this all comes from the Visudhimagga's explanation of jhana. I'm not sure there's any references to a term similar to "advert" in the Canon, but I keep running into the term advert without any further explanation in plain English of what that means, and it's a rare kind of word to begin with:
Following this the meditator should try to acquire five kinds of mastery over the jhana: mastery in adverting, in attaining, in resolving, in emerging and in reviewing. Mastery in adverting is the ability to advert to the jhana factors one by one after emerging from the jhana, wherever he wants, whenever he wants, and for as long as he wants. ...
The definition of advert:
1: to turn the mind or attention —used with to <adverted to the speaker>
2: to call attention in the course of speaking or writing : make reference —used with to <adverted to foreign-language sources>
Mastery in adverting means mastery in turning your mind to the jhana factors? So the first step of jhana mastery is the ability to turn your mind to:
- applied thought,
- sustained thought,
- happiness and
--after you've emerged from jhana?
So after I emerge from jhana, I have to turn my mind to applied thought, then to sustained thought, then to rapture, etc. when and for as my mind wants to, no matter where I am.