Does Time Machine use internet?
Time Machine does not use the internet, but iCloud does. If you use an iPhone or iPad, iCloud will backup the images to iPhoto, and that can use significant bandwidth. 

Calendar, Mail, Contacts, Messages, Notifications, Twitter, etc all use bandwidth, and all are on by default. iCloud will also backup your documents and data, if you have configured this. If you have more than 10GB of files in your Documents folder, iCloud could be simply backing them up from the new hard drive.