but him saying that baba is the underboss seem to mean that it's set before hinamatsuri, or at least before the promotion incident.
J<->M is explicitly set after Hinamatsuri. We have references of Mao being an active celebrity.
You're confusing things a bit. Baba was promoted to head of the Ashikawa family during the events of Hinamatsuri. Which is under the Oudou Alliance. But as far as I remember, Hinamatsuri never really gave any info on his personal standing within the Oudou Alliance as a whole.
Come J<-<M, Baba is apparently now the underboss of the Oudou Alliance as a whole, so good for him I guess. The man is putting in the work. (Or most realistically, letting Nitta and Hina do some shenanigans behind the scenes while taking a lot of credit for it).