As unintuitive as it might seem, you cannot directly compare disk utilization on a Time Machine drive to the source system. That's because of the way Time Machine stores its point-in-time backups.
Each snapshot (of which there can be many per day) is really a diff from the previous one, so will depend heavily on the amount of data that is changing between each backup. If you change large files (such as video files), these will consume a larger amount of your backup drive (for example, you may have several copies of that 100GB movie file on your backup drive as you've worked on it over the day, even though you only have one file on your system drive).
That said, doubling the host system's drive seems like a lot for the first day's backup, but I still wouldn't worry about it. Time Machine has proven to be quite resilient in my experience and I just let it do its thing.