You hit them just as they are going out of range/you get CCed/whatever. They run away. Normally from that moment on - assuming they used a dispel on themselves to get rid of any DoTs - the out-of-combat would kick in and by the time they get behind a pillar or somewhere LoS to drink they are already ready to drink, instead they have to wait those 6 seconds, THEN get the out of combat timer. If you include the time it takes for projectiles in flight, you are likely looking at just under 10 seconds extra on top of the normal amount of time it takes to start drinking. Plus the few seconds it takes of drinking before it even begins returning any mana.
Those extra <10 seconds on top of the normal time means that getting drinks of will be insanely difficult to do. If you let a healer have that amount of time free and get nothing out of it, then that is your misplay. Even if its only getting a bunch of CCs out of your opponents so that when the healer finishes drinking everything is on DR, or you get a defensive cooldown out of your enemy, any number of small advantage can be gained. In arena, 10 seconds is quite a long time.
NB: Of course if I am wrong and the Mastery does have LoS and range requirements to work, then this isn't actually a thing, I'm just going by what appeared to be happening in beta streams I have watched. Really could use a confirmation on this.