If you use DriveHQ FileManager's folder synchronization feature and if you don't want _DHQ_Sync_Cache_ folders being created, you can click on Tools --> Manage Synchronization. It will display a list of synchronization tasks. Select a sync task and click on Edit to edit the synchronization task. You can uncheck the check box "Save a backup copy of automatically deleted files".
It is not recommended unchecking the check box. Please note Folder Synchronization is not the same as Data Backup. If you accidentally delete a file in a synchronized folder, FileManager will delete the synchronized file in the other folder. This could result in data loss. If you don't uncheck the checkbox, then you are better protected.
Of course, if it is for data backup, please use DriveHQ Online Backup client software. DriveHQ Online Backup will never automatically delete your files.