I looked at my frog demons in GM editor mode with DFHack, discovered something. The frog demon I embarked with, as well as the frog demons born in my fort, all count as historical figures and have historical figure IDs. The frog demons that come in with migrants, however, do not count as historical figures and have IDs of -1. Finally, when I turn on "allow setting labors on anyone" in Dwarf Therapist, I can enable labors on the frog demon babies born in my fort, but not on the frog demon babies/children/adults that migrated. The Fiend I embarked with also has a historical figure ID.
I have no idea if this specific ID has any effect on setting labors, but there it does seem to indicate the problem lies with how the creatures that arrive with migrants are treated. The game seems to consider them pets in this case. I need to try buying some from merchants and summoning some from the circle to see how those are treated, but my guess is that there is something involved in their generation that makes them count as pets and prevents them from being used as citizens.