I'm not sure about which word people in Central Vietnam use to indicate the umbrella because there are lots of dialects along this region. People in my hometown (Hue City) use "dù" more commonly than "ô". And yep, raincoats (áo mưa) are more popular than umbrellas in my hometown, too.
While I agree to a certain extent, let us be fair. The program is meant for foreign speakers. The Northern speech is much easier for a foreigner to deal with. To start, they actually pronounce everything, whereas we Southerners muddle some of our speech (d=gi - just an example). Moreover, I think the "official" Vietnamese accent is a Northern one, so it's the one that should be taught.
All that said, I admit to dragging my feet on progressing. It gets frustrating to go through a lesson and getting things wrong because terms like "nhà ga" is being taught while I learned "trạm xe lữa." Ultimately, while I can say that I want to improve my Vietnamese, it's hard to find the motivation because my day-to-day communication uses the Southern dialect.