does this mean that PtL "resolves" (gives stress) before his free action kicks in
No, not unless you chose to resolve it that way.
The trigger for Jake, PtL, Experimental Interface, ect... is after an action which is the same timing for gaining the stress. That means you have the option on what order to resolve things in.
So you can chose to use that trigger of "after" for PtL or other actions that trigger on it, before you receive the stress from PtL.
That I absolutely understand, but that was case before the recent FAQ since it was covered by "If a player has multiple effects that resolve at the same time, can he resolve them in any order? - Yes."
What is the new PtL FAQ addressing?