Somehow it seems like you may be tapping something too slowly, or in the wrong place, when switching apps... and the phone thinks you're trying to select an app for multi-window (which would put one app in top or bottom half of the screen, allowing a second app in the other half).
Try going to Settings -- Notifications -- Overflow Menu (three dots upper right) and select Show system apps -- System UI and making sure that if notifications are turned on, Multi window is turned OFF. Back out and try it again. Let us know if that stops the pesky notifications.