Any contacts or media backed up to any Cloud service (e.g., Verizon Cloud, iCloud, Google Drive, etc.) are not transferred by the Content Transfer app and need to be restored to the device using the same service. The Content Transfer app only transfers contacts, media, etc. to the new device that haven't already been backed up to a cloud service.
For a quick overview, watch this video.
For additional info on backing up or transferring media content, refer to Transfer Content Between Devices.