If you restore a backup using iTunes to an iPhone (or iPad & iPod Touch) that already is setup and has apps installed on it, the apps will still be installed after the restore finishes and you setup the iPhone again.
This is true for restoring ANY backup, not just backups filtered with Decipher Phone Refresh or Decipher Activity Transfer. The reason for this has to do with the way apps are handled in a backup.
The apps themselves are not backed up. App data is backed up, along with a note to download and reinstall the app from the App Store after the iPhone is set up again. That's why you see those grayed-out icons at first after you set up a new iPhone; that gray icon is the temporary state while iOS downloads and installs the app again.
Because Apps are not part of the things that are backed up, they're also not deleted when you restore. When you restore a backup, the restore process doesn't delete any apps that are currently installed at the time you restore. All of the app data is deleted and replaced with the backed up app data though, because that IS backed up.
We typically recommend starting from a blank iPhone to restore the cleaned backup. However, we know how hard it is to press that Erase All Contents and Settings button! You can restore the cleaned backup once to see that it worked, and then wipe the iPhone and restore the cleaned backup again, if you want to test the restore before wiping!