4 new schools each play 7 games against old schools (7*4 = 28 games) and 2 games each against new schools (4 games total)
10 old schools each play 2 games against new schools (10*2 = 20 games)
That means new schools will play 28 games against old shools while old schools would play 20 games against new schools
I will concende that I didn't think through things completely or actually do the math behind it.
Maybe the 4 new schools will each play 6 games against "old" schools (6*4 = 24 games) and 3 games against each other (6 games total)
That leaves all 10 old shools playing at least 2 of the new schools (20 games) plus either 2 teams playing all 4 new schools OR 4 teams each playing a 3rd new school. Either way I see your points. I'm guessing they have every team play at least 2 of the "new schools" but some will have to play 3 for it to work out for a 9 game schedule.