It's not passive 1200 agility. The proc lasts 20 sec, and it stacks 120 agility every sec for a max of 10 stacks. So your agi looks like this during every second of the proc:
1:120
2:240
...
9:1080
10:1200
11:1200
...
19:1200
20:1200
21:0
22:0
http://db.mmo-champion.com/s/108011/f = the 20sec proc that causes you to gain stacks of agility
http://db.mmo-champion.com/s/108016/b = the stacking agility
You can compare it to
http://db.mmo-champion.com/i/50348/d from ICC which works in exactly the same way. As soon as the "parent" proc fades, the associated "child" stacks fade as well.