Yes, if you publish as a webpage via github (github pages), it's public.
You can not serve a file directly from github except using github pages. But if you use github pages, then your file will be public.
On the other hand, the tiddlywiki github save feature can work independently of the publication feature and can save to a private repository. In that case, when you want a copy of the latest saved version of your file on your hard drive, you will need to do a download. To do that, you navigate to the file inside of github and click on it. There will be a "View Raw" link. Right click on it and select "save as" to download a copy.