After I've beaten the Rift Guardian and grab the loot, I teleport back to town and talk to Orek to get the gold and experience. Then, there's a countdown for about 30 seconds while the rift portal stays open. I go through the portal again, but I find that I'm at the entrance of the rift, with the enemies cleared out, naturally. Then I run around a few seconds before I'm taken back to town again.
Why does the rift stay open? What am I supposed to do?
It stays open for a bit because that is just how its designed. You are not supposed to have to do anything.
Think of this as a bit of forgiveness if you talked to him by accident but needed to go back in and grab an item real quick. This gives you that moment to handle the Oh Crap I have to go grab that legendary I didn't have room for! Or, for other people to be aware that the rift they are in is closing on them.
There is no specific 'they are giving you time to do something' aspect here.
