Yesterday I was taught on how to taste tea in this manner. In general, the method can be used to taste other liquids such as water, juice, wine, etc.
Basically, your upper lips should not touch the cup. Your lower lips to be intact with the cup. Suck the tea directly into the end of your tongue and let it flow gracefully down the throat. The taste at your throat defines the 'After taste'. The longer the 'After taste' the better the quality is.
While sucking the tea. There should be this sucking sound. You should not tilt your head up. The cup should remain horizontal. The tea should bypass your teeth and front portion of your tongue directly to the back of your tongue. The tea should not be spread out throughout your mouth. Once the tea is at the back of your tongue, let it flow into your throat. Don't swallow it.
Tea Tasting is much easier when tea is hot but not burning hot. Temperature around 60-80 degrees should be fine. You should not burn your tongue if you sucked it to the back of your tongue correctly. Also when doing tea tasting, you should stay focus and do not talk.
Not an easy task... Burnt my tongue and choked cause sucked too hard. Need a lot of practice