Now I started seeing the source of my confusion. The phrase "annotate the most recent continuation frame": I interpret it as modifying the most recent continuation frame to attach the annotation. But it's not---I only need to keep the "current" dynamic list of marks, and when the next continuation frame is pushed, that continuation frame remembers the tip of the marks so that it will be restored when the frame is popped.
It might be helpful to say "_effectively_ annotate the most recent continuation frame" to indicate that annotation doesn't really involve immediate direct connection between continuation frames and marks.
If I understand "dynamically annotated", it is less likely that I would've thought with-continuation-marks could modify the existing continuation frames. But it might be helpful to add a hint that continuation frames are immutable.