Considering he seemed to be physically cut into pieces...
perhaps we can find the answer in another primal we know was cut into pieces: Anima.
Actual limbs of Anima were upkeeping the towers and drawing aether towards the primal's core, but once we defeated the core, all the pieces just disappeared.
I heavily suspect the same happened with Zodiark. The moment the Source part of Zodiark was dead, all the pieces on the shards would just cease to exist.