First, as Spotify indicates, this service is really intended for a single user, potentially using several different devices. Therefore, any song, album or playlist added to the library (My Music) gets recognized by any device logged in using that account and will be seen by all other devices. Thus, anything that my daughter adds to her iPod will show up under My Music on my android.
Second, I think what probably happened on my phone is I hit the offline slider under the "Songs" tab and thus any song added from any device downloaded for offline play. I uninstalled the Spotify app from both my phone and my daughter's ipod. When reinstalled, no offline sliders were on by default and no songs on either device were downloaded for offline play.
So, it's possible to have different songs downloaded for offline play on different devices by selecting available offline by album, artist or playlist.