What you experienced is expected behavior, but I can definitely see why it's confusing.
When you use the main CHS window to initiate the modification of the text of a clip, it updates the clip but doesn't put the new clip onto the clipboard.
However, that's not hard to do -- there is a little orange clipboard icon just a little bit left of the "Modify Format/Case" button you can press to put the clip you are editing into the clipboard:
Now you might think that is too much work to do -- but that's only because going through the main window is not meant for efficient quick changing of text to be re-pasted.
If you want to set up a fast efficient workflow for modifying text that you plan to quickly copy and repaste, you should use the quick-paste menu (ctrl+alt+q hotkey by default), and then choose 'T' for formatting presets -- where you can quickly copy the selected text and apply one of your saved formatting presets, or choose the last option to invoke the modification dialog on the selected text.
With that option you can very quickly modify the selected text AND it will automatically put the modified text on the clipboard (and in fact try to paste it into your current app).
Once you get the hang of that, CHS can be very convenient and quick for making frequent changes of text.