Caffeine content in tea depends on the cultivar, method of cultivation, and age of the leaves (shade-grown buds and young leaves having the most), but not the general type (black/green) of the tea.
Black tea is withered/oxidized before being dried, whereas green tea is usually roasted (for Chinese tea) or steamed (Japanese). This processing does not significantly change the caffeine content. Any difference between black and green tea produced from the same leaves is due to differences in brewing - green tea is usually steeped for a shorter time than black.
Shade-grown tea is very expensive (usually grown for matcha or gyokuro), and cheaper tea is made from the older leaves, which have the lowest amount of caffeine. It's therefore probable that this tea is naturally low in caffeine.