Would it be possible for you to provide a link to the page in question, please. As, the next line should be indented automatically.
For example, I have just this moment added the Text Module to a test site of mine and added a basic unordered list and when I reduce the browser width, at no point does the text align with the bullet. All I end up with is:
* This is our first line of
text in the list.
* This is our second line of
text in the list.
* This is our third line of
text in the list.
Also, please, bear in mind that I wasn’t using an image for the bullet, so it is most likely related to that. So if you can provide a link, we will be able to assist you further.