When speaking about Ground-types, if we look at the Groud-types, we have, usually, they're either:
a) animals which live in the desert
b) animals which live underground
c) things actually made of dirt.
Zygarde does reside underground in a cave. But in its case, we can't just base it on that... When I ask why it is Ground-type, I'm talking more about the symbolical meaning. For example, the most accepted explanations for Dialga and Palkia's types are that diamonds are one of the hardest substances in the world, hence Dialga's steel type; and pearls are formed in the sea, hence Palkia's Water-type. So, in that context, why is Zygarde, a being capable of taking various shapes because it is made of various small organisms, a Ground-type? How does the Ground-type relate to genetics? Psychic or even Normal type seems to fit better to me...
Or is it because of the underworld association? That sounds more like Dark-type to me...
Speaking of which, Zygarde is supposed to be the order pokémon, the one that keeps balance, but the Perfect forme looks like it's going to destroy the whole world, imo. Yveltal compared to this is just a blind bird with a bad attitude...
(this is actually something I've been intending to overanalyze some time, figuring as specifically as possible what each type is about and what is just an extra flavor that is shared with other types etc. and I find that Ground is one of those that's harder to pin down to something specific)
I'd change "b" to "making use of the ground", like digging (Diggersby, Trapinch, Sandshrew, Drilbur, Diglett, Onix, Nincada..)
as it goes from "lives where" to what the actual concept is about, a somewhat solid floor beneath your feet (it also takes over pretty much all the desert pokes, which is also a good thing due to the deserts harboring quite a diverse type spectrum from Grass, Fire, Psychic and of course Rock types.)
but it feels there is still something crucial lacking when you look at a list of Ground types that's hard to describe.
I'm talking about Rhyhorn, Donphan.. Stunfisk even. ...they're just generally very tied to the ground? or at least moreso than non-Ground pokes. Constant contact with noteworthy bodyparts?
Either way, my point being, I see Zygarde as fitting for a Ground type as them and Nidoking, Mamoswine etc.
I mean, I don't see it doing sommersaults (apart from the 10% forme now I guess XD), it just snakes along the floor elegantly the whole time.
As for the conceptual connection. One thing is, Zygarde is about protecting the environment from imbalance. But also the underworld association as you say. Underworld can imply underground just as well as it might imply something more mean-spirited IMO.
But at some point, you could just as well go "How is Suicune a Water type?", sure it has a stereotypical blue colour slapped on its body, but that's not a reliable dstinction. It having associations with wind, the aurora borealis, and learning a lot of wind-based and just as many Ice-type moves as Water moves doesn't make it better. It's just a random example of the fact that sometimes a Pokemon is a certain type because whoever created it saw that as its element. Meaning being a certain type is the reason why it's good at it. It can go both ways, design aspects/behavior ---> appropriate type, a type ----> appropriate design aspects/behavior.
EDIT:
I forgot an important point here.
When it's about groups of legendaries, like trios and mascots, their types are often of equal importance between them.
So for example here we have Xerneas, Yveltal and Zygarde.
Xerneas and Yveltal themselves are intended to be perfect counterparts.
So their main types reflect that: Fairy VS Dark.
But Yveltal has Flying attached, for the simple mundane and undeniably obvious reason: it just happens to fly.
So in THIS CONTEXT, Zygarde being Dragon/Ground, I don't think the Ground type is supposed to be of some very deep and elemental importance, but is rather just the obvious addition to it's main type, in order for the three of them to be from separate realms.
Yveltal the Dark type - Sky ----> /Flying
Xerneas the Fairy type - Surface ----> /nothing
Zygarde the Dragon type - Underground ----> /Ground
It differs between legendary groups of course, so you cannot contemplate them in the same manner as when looking at the Unova Dragons. Those for example share the fact that they're primary Dragons, with their distinctive feature being what element they represent in addtion to that.