Hello, CM!
The javascript embed code will not change, so you don't need to paste any new embed code onto your website.
When you embed your survey using Javascript, then visit the survey, you are cached in that version of your survey by a cookie (a variable) placed on your computer. You won't see changes made to the survey.
What you'll want to do is clear your cache and other temporary internet files, then reload your page and you'll see the new version fo the survey.
We do this because, imagine you're in the middle of a survey and the survey creator moves a required question from page 2 to page 1 while you're already one page 1, then you click to page 2 – you would miss that question entirely if we didn't cache you in the version of that survey that you've started.
I hope this helps!