If I tap in the center of the screen, the notification bar doesn't show up with the navigation bars, I instead have to pull down from the top to see it.
I am using Adobe Acrobat on my Android phone and tablet with the same issue.
Are you talking about the device's notification bar (not any Acrobat provided menu)? If so, that is the correct behavior. Acrobat is designed to make the document as readable as possible, so it therefore displays the PDF full screen.
Retrieving data ...