Maybe the Vesuv player embodies and ancient god related to fire, earth and disaster/protection. Therefore, they have power to control the elements and bend the volcano to their will (to a certain degree).
Perhaps, their actions are made more powerful the more they are revered in Pompeji (Gameplay connection).
Many gods were revered in Pompeji. Maybe this could be a aspect that connects both players. (Gameplay connection).
Goal:
Prevent the Vesuv from erupting or buy as much time as possible for evacuation
Gameplay interactions in detail:
closing magma rifts shut
forcing magma down a rift
lowering magma temperature & solidifying it
thickening the clot
alleviating pressure/gasses
Ties to the other player:
The more time you can buy them, the better prepared they will be when the volcano erupts.
They may be able to evacuate the entire city before the eruption.
Ideas
Goal:
Gameplay interactions in detail:
Ties to the other player: