I can only speak from the experience of having one subscription to Sports Illustrated in the Newsstand folder, but this is how it works for me.
I receive a notification every week that the new edition is ready to be downloaded. I must then go in the SI app in the Newsstand and initiate the download of the magazine on my own. When I tap on the bottom of the screen - in the SI app - a toolbar pops up. I tap on Store, sign in and then have access to all of the magazines that I want to download.
Try going into one of the apps - assuming that you have multiple apps/magazine subscriptions - and tap on the bottom of the screen to see if a tool bar pops up. Tap on the top or the sides as well as some apps may have the tool bar in those areas of the screen.