Return of the Good, Bad, and Depends-On-Circumstances!

[Proginoskes]

... people or animals who appear because of it are not the actual thing ...

Er... See the Sailor Moon teaser Bob posted about the song Starlight Express...

That (and any other deity) is a special case: recall what happened when Doug used With a Little Help From My Friends to create simulacra of Shadowwalker, Kat, Silverbolt, and Wetter Hexe (DWII Chapter 12). A deity's awareness automatically inhabits a simulacrum; in all other cases, a simulacrum's mind is built from Doug's memories of the original person. Unless the simulacrum is of a deity, and the deity opts to stick around, it vanishes at the end of the song.