There is a small gap in time between when an ability is used and it reaches its target, similar to flight time of say a fireball spell. When you press rip if you watch carefully you can see a delay between when the energy and combo points are consumed compared to when the rip effect is applied to the target.
The damage calculation for rip is done both as the energy is consumed, and again when the debuff ticks on the mob. Basically, if you wait until mangle has less than one second left, and you "release" rip while the mangle debuff is up, damage is calculated as if rip has mangle. Half a second later, mangle wears off, then rip reaches the target and is applied. The rip damage has already been calculated with mangle up, so it continues to tick for an extra 30%. If now you were to mangle again, the rip damage is increased again.
Cycle:
0.0: Mangle
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Generate combo points
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11.5: Rip "cast", energy and combo points consumed
12.0: Mangle wears off
12.1: Rip debuff appears on target
12.5: Mangle before first rip tick for double effect
Something to keep in mind is that the last mangle at 12.5 seconds does not need to be there for the phantom rip to take place. So if you were out of energy at 12 seconds, the first tick of the rip will tick as if only 1 mangle were on, and you can apply the "second" mangle any time in the future, or not at all. This method requires that no one else is mangling, because it will make timing very very difficult.
Through much practice I have been able to become quite successful at getting double rips varying on different bosses. For example, something to do with the hit box of Anetheron makes it extremely difficult to get double rips. While Rage Winterchill is a much easier target. Although I originally experimented on the servants in the Blasted Lands, I found that they also are more difficult to time double rips on
I hope this clears some stuff up.