Thanks for sharing the map. I can click on the parcel and get it to pop up the data. Though, like you said, the buffer is on top of it. Clicking the next arrow will show me the parcel data. This might be a little training thing you might have to do with the people presenting this map (showing them the arrow).
According to this thread, there is no way to change the order in which the popups come, unfortunately:
How can I change the order of popups on an ArcGIS Online Map