Vatican II didn't ask for the Novus Ordo Missae. It was the product of Bugnini's Consilium after the Council.
Yes, V2 asked for a reform of the missal (which happened afterwards). Same with Trent asking for a codification of the missal (which happened afterwards...Quo Primum happened after Trent).
V2 didn't give all the gory details of what Bugnini had in mind for the new mass; it only mentioned that the liturgy needed to be "updated" for the "people's of God" and "greater unity" (i.e. meaningless, modernistic phrases).