Q: split view just goes to full screen?

I just upgraded to El Capitan - partly to take advantageous of Split View.   When I hold cursor over the green button with arrows the window just goes to full screen (fills the page).   I have read some support and have gone into Mission Control and checked off the box regarding 'Displays have separate spaces.'   And I have logged off and on after doing that.  There is no change.   I still can't seem to get Split View to work.   The same thing happens: doc moves to full screen.