Osmanthus fragrans aurantiacus (orange rebloomer)
I went to Nurseries Caroliniana website to see if they have any latest pictures of Beni Kin Mokusei in blooms but they didn't. I happened to notice that they are selling reblooming orange osmanthus. From the description - "The leaves are not as stiff as the selection of "aurantiacus" that we grow, but one outstanding characteristic of this selecion is the new growth which is a deep burgundy. Even each succeeding flush throughout the growing season shows the burgundy color on the new growth."
It sounds like Yue Yue Hong cultivar from China. http://forums2.gardenweb.com/forums/load/trees/msg0700004019047.html