Seems to be a reincarnation of this status-completed issue from early last year: When opening the app through push notification, the inbox is cleared and not shown.
I'm on Android 5.1.1 and my Stack Exchange app is version 1.0.73.
If I open the application through a notification it opens with the inbox sidebar open, but there is no content inside. The loading graphic doesn't display, either, as if to suggest that loading never gets kicked off. To view the notification properly I then have to close the sidebar and reopen it: