Some Jasmine tea is simply tea leaves that have been harvested, prepared as green tea, and then jasmine flavor is added.
Higher quality Jasmine tea, like Two Leaves and a Bud's Jasmine Petal Green Tea, is harvested in April and May, and when June arrives, the tea is spread out for five nights and the Jasmine flowers that bloom that month are laid on top of the tea. Tea absorbs odors very easily, and so during the cool nights, the premium green tea is basking in the floral scent, building up a nuanced taste profile.
If you've never had this quality tea, it's a revelation when you taste something like two leaves and a bud Jasmine Petal green tea. This is the sort of tea you taste as much with your nose as with your tongue, as its delicate, flowery Jasmine flower scent lingers over the cup.