I believe it wakes them as appropriate. Acheron will always wake, Abashi will if the Sheaim are around, ditto Driffa for the Illians, and if the owner of the OO holy city follows OO, I think they'd get Thalawhatever.
Does that mean if the Ilian say did the Stir from Slumber ritual, that the appopriate dragon spawns in the appropriate place? The Ilians get Drifa, Sheaim get Abashi, Kuriotates get Eurabates?
Are there any more dragons besides Acheron out there? I know about the Octopus Overlords one.