ParallelSpace and DualSpace use the same technology if I get their description correctly and this technology has nothing to do with virtualization: they use app cloning
App cloning means that an app is renamed (not the visible name but the app package name such as
com.whatsapp). Therefore the app is unpacked, modified at certain points to use the new name and then packed and signed with a new signature and afterwards installed.
As Android separates each app a renamed app can be installed side-by-side with the original app. The actual separation is done by the Android OS in exactly the same way it is done for every app.
And just like any other app if the repackaged app stores data in the sd-card section you can access this data.