1. TM backups are not clones of your OS X installation, if you want clones use Carbon Copy Cloner or Super Duper.
2. Parallels asked you for activation because it recognized it's running on different hardware.
3. If in the settings of the VM the "do not backup with time machine" is activated, the VM will not be backed up to TM.
4. Bootcamp based VMs cannot be backed up with TM, or cloned with CCC and SD. They reside in a separate, Windows partitions, they can be backed up with Windows specific utilities, or cloned with Winclone or Acronis True Disk.
5. (to Honzall) It's true that the virtual disk in a VM is a huge binary file, however Parallels has introduced technology to minimize the impact of this on backups, there is an option to "optimize for TM backups" (smart guard is a different thing, it's automated snapshots), which splits the disk into smaller files. However I also prefer to exclude my VMs from TM, and simply copy the pvms.
6. If you still have access to the old disk you can still copy the VM.
Last edited: Nov 27, 2014