The text indent does indeed move both rows of text, but it should align both to the same left margin. That is, it controls the indent of all the text, and thus ensure that all the lines of text line up the same.
How are you making the bullets? Are you using a template with a bulleted body, or are you using a text box?
And just to be clear, you do want a hanging indent for your bullets, such that the bullet itself hangs outside the bullet text, which is all aligned to the same left margin?