However when the timer reaches 0 the name of the rift changes from it's current rift name (eg. Advocates...) to "Nephalem Rift". If you click the portal at that moment it will open a new rift where you can kill enemies and the rift guardian.
Doing this won't give you the the quest nor the completion bar, but everything else works.
So essentially you get two rifts for 5 fragments. But seeing as many fragments we get it's probably nothing big, just thougth I'd mention it.