Thank you careyh!
Did you uncheck "Allow file contenst to override Tab and Indentation settings" under Global > Editor > Indentation?
I tried both unchecked and checked, it does not seem to affect the behavior. But it still did not apply TABBING changes project-wide.
Also I noticed that the Apply button can replace the need to reopen Edit->Current File Preferences->Editor->Indentation. Simply checking "Prefer Tab characters over space" and pressing Apply and then unchecking it does solve the issue in the file. And it remembers it no matter whether the file was Saved or not.