When the notification pops on screen, you are granted the rewards. If your OS is not able to show the notification (due to Focus Assist, DND, or some other reason) then you are not rewarded (a future update to Brave will let users control visibility from within the browser entirely).
I believe the question was about the mechanism by which you viewing the ad is reported to Brave, not how the ad display was implemented. (A weird interpretation of "reported".)
Our Rewards server distributes virtual tokens to the instance of Brave (which has an associated Payment ID). These tokens can be exchanged when ad notifications have been viewed, and when other ad-related events occur. The tokens aren't tied to any user information.
Not to nitpick, but you still didn’t answer the question. I don’t think anyone is confused over the concept “view ad -> get token”. The parent comment was wondering how you determine an ad was viewed.