That’s all it ever means. Treat it like any other word. It’s never attached to another word. There’s always a space on either side, unless the ellipsis is the last word in a sentence in which case it is followed immediately by the punctuation that ends the sentence.

Eg.: I can’t believe ...! (In this case the omitted words might be “what I just saw.”)

Eg.: I can’t believe ... how stupid that is! (In this case the ellipsis might indicate the omitted words “for the life of me.”)

Your usage in your first example is inappropriate (or, so it seems) because I can not determine what words may have been omitted that are indicated by the ellipsis. All you need there is a comma.

Eg.: As the man walked, he looked for his dog.

-Laelth