The notification about these Purchase Requests is sent in real time to the Family Managers, and they could decide to either deal with them right away or let them wait their turn in a virtual queue.

The new Purchase Requests feature in a nutshell
The completed purchase will be saved in the Order History, just like a Family Payment purchase, and the happy child will receive a confirmation email on their Google account notifying them that they can have their fun.This new Purchase Request feature works for paid apps on Google Play, as well as in-app purchases, so your kid can get that Fortnite skin and brag in front of other nerds about it. At the moment, this doesn’t work for Google Play Books, Google TV, or subscription services. The new feature is currently rolling out, and you should be able to see it in the Family Link purchase approval settings.
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