ROZ-mə-ree is a chiefly British English pronunciation (and by extension used in Australia, New Zealand, etc.), whereas ROZ-mehr-ee is used in American English (and I believe in Canada as well).
The listed pronunciation is basically ROSE-Mary. The upside down e is a long a, like in air or Mary. This name is absolutely beautiful, as are nearly all the ros- names :) theres quite a few nicknames too, like ro, rose, Rosie, or Mary. I like it as Rosemary or Rose with the middle name Mary, or even Rose-Mary. Whatever floats your boat =P I just really wish this name would become more popular along with the other ros- names!
Well, this is weird. I'm not entirely sure what the listed pronunciation means... It looks like Rose-Marie. Marie being mə-REE (at least where I'm from) and Mary being MER-ee, it seems like this name should have two places of emphasis or something like that. I've always pronounced Rosemary, ROZ MER-ee. Like Rose Mary, but without a pause.