There are two options for Tetra's daemon and it realy depends on what effect the Neath has on the whole thing. Are there more people with bat and weasel daemons in the generations after the fall? Does the unnatural fauna of the Neath lead to daemons settling in less 'realistic' forms?
If Tetra had grown up on the surface, es daemon would be a black guillemot, but being Neath-born (and not entirely human), Tetra is at home down here in a way that just doesn't suit a bird daemon.
It might still have happened, if the whole near death/shapeling necromancy thing had damaged their bond. Tetra's once-human self changed and left the daemon behind with the memory of what they used to be. Eventually it takes the form of a surface bird, and the two of them are often seen apart, because they're not quite each others' any more. Two beings connected, not one in two bodies.
In a happier world, they're both equally affected. Tetra's (Hitch's) daemon is visibly Neathy, tending towards amalgamous forms with unusual numbers of eyes or heads (would that affect how people see en? or would it have been fairly normalised by that point?). Eventually it settles on a sort of aquatic badger with the features of a lampcat. A fairly ordinary creature, by the Neath's standards.