I may have found a simple way to fix this quest.
In "FamiliarExotics_Chapter2Quest.lua" located under [YourPath]\Sid Meier's Civilization Beyond Earth\assets\Gameplay\Lua\Quests
The relevant line should be:
local newObjective = AddObjective(quest, "QUEST_OBJECTIVE_BUILD_BUILDING", VIVARIUM_TYPE, 1, city:GetID());
Simply removing the city requirement thus changing it into:
local newObjective = AddObjective(quest, "QUEST_OBJECTIVE_BUILD_BUILDING", VIVARIUM_TYPE, 1);
Should cause the quest to be completed by building a Biofuel plant in any
(don't ask me why the variable is called "vivarium_type" it is in fact set on the biofuel plant)
local VIVARIUM_TYPE = GameInfo.Buildings["BUILDING_BIOFUEL_PLANT"].ID;
Perhaps initially it was intended to be a vivarium ("BUILDING_VIVARIUM")? That would make the quest a lot more easy to complete. Another solution could be to change this line instead so the requirement is a vivarium and not a biofuel plant.
This should be worth investigating if it actually works, I have no time to test it now.