I don't see a problem with the <sub> & <sup> tags. They seem to work just fine for me on Sigil 1.0.0 on Windows 10. You may need to check any CSS files you have linked to your html file, or if there is any styling at the top of your html file, or if there is any inline styling, to see if you are overriding the Sigil defaults.
Look for:
Code:
In a CSS file or in the <style> section at the top of the html page:
sup {font-size:...}
sub {font-size:...}
In the actual HTML document:
<sup style="font-size:...">yadda yadda</sup>
<sub style="font-size:...">yadda yadda</sub>
If you could show an example of the html and CSS you are using it would help us to help you.