I emailed their support and got this answer:
Unfortunately, this type of usage is likely due to the heavy usage of compression within our code base. We have a bug ticket open to address this type of usage in the next milestone release of Jungle Disk. At this time, we simply don't have a solution for the high CPU usage.
As a work around, you can switch your backup to a Legacy Backup. This would eliminate the compression that Jungle Disk is performing. However, note that a Legacy Backup does not perform any compression or de-duplication. In addition, you would need to re-upload your data.
Simply go to your Jungle Disk client configuration and define a Legacy Backup.
Seems to have been solved with a later version.