I am unaware of the source you cite here, but and I couldn't find any direct references to diegesis in my generic rhetoric resources (Sloane's Encyclopedia, Halsall's Dictionary of Literary Terms, or Silva Rhetoricae). However, the exercise in narration in the Progymnasmata is similar to diegesis. Both Aphthonius and Hermogenes make the following comparison (I'm using Hermogenes' description found in Kennedy's Progymnasmata: Greek Textbooks of Prose Composition and Rhetoric😞
"A narrative (diegema) differs from a narration (diegesis) as a piece of poetry (poiema) differs from a poetical work (poiesis). A poiema and a diagema are concerned with one thing, a poiesis and a diegesis with many; for example, the Iliad is a poiesis and the Odyssey is a poiesis, while the "Making of the Shield" (Iliad 18) and "Descent into the Underworld" (Odyssey 11) and "Killing the Suitors" (Odyssey 22) are poiemata. Again, the History of Herodotus is a diegesis, as is that of Thucydides, but the story of Arion (Herodotus 1.23) or of Alcmeon (Thucydides 2.102) is a diagema" (75).
Thus, it appears the narration (diegesis) is a whole, made up of narrative (diegema) parts. The narrative exercises in the Progymnasmata would thus train students in the parts of narrative that could be combined into larger narrations (dramatic, historical, or political; to use Aphthonius' division). For more complicated varieties of narration, I can copy and send the entry on "narrative" from A Dictionary of Literary Devices: Gradus, A-Z, which includes a complete technical exposition.
Pedagogically, it seems, narration is quite different from socratic teaching, since narration does not engage in dialogue in media res, despite its reproduction of direct speech and dialogue. The closest identification of narration and socratic teaching would be Plato's dialogues, which are written after the fact (narration) as dialogues containing a great amount of dialectic method on display (questions--maieutics; and refutation--elenchus).
I'm ignorant of Charlotte Mason's explanation of narration, but from within the Platonic method, I'd say that narration would dovetail with dialectic pedagogically. We see this in his dialogues, and it occurs in different orders. In Gorgias there is an opening question, which is developed through dialectical exchanges with five separate characters, but predominantly through Socrates and Callicles. At the end, after much frustration, Socrates resorts to a myth in order to establish ethical force to his unaccepted (at least by Callicles) refutation. In Phaedrus, however, a speech initiates the dialogue and culminates in a lengthy speech that includes a myth, which then gets explained and applied in a subsequent dialectic discussion between Socrates and Phaedrus. The narratives (not narrations) serve to illustrate and support the arguments and ideas, but they can precede or follow in order. As an interesting additional point, it is my belief that Phaedrus, as a dialogue, presents itself as an example of the method the dialogue sets forth, and thus serves as an example for imitation.