Easier to expand here than on Twitter.
Yes, I'm talking about the "Options..." button. In general, the "On successful completion" option should be "Do Nothing".
Note that, if misconfigured, you wouldn't necessarily be able to tell from the "What's going to happen?" section of the Scheduled Copies window, because it's not as detailed as the real one.
What you can do is use File > Load Settings... to open ~/Library/Application Support/SuperDuper!/Scheduled Copies/your-schedule-settings. Once loaded, look in Options and see if you have something set there. If so, quit SD!, restart it, delete the schedule and recreate with "Do Nothing".