Strum all strings all the time, or...?

I found tabs for "I'll Fly Away" and "Go Tell Aunt Rhodie" - both in D for a DAa tuned dulcimer. They only show the melody.  Should I only strum the melody strings, strum all the strings all the time, or selectively add the drone strings.  When I strum all the strings on every note it sounds rather sitar like.