My apologies if the following was addressed already in-game:
The Fate Point economy seemed wonky in this session, especially in combat. From what I remember, Adam was taking Fate Points spent by the players to invoke aspects (their own, situation, or NPC) and putting them immediately in his NPC pool. As far as I can tell, though, during a scene the NPC pool should only increase if players compel an NPC aspect.
Fate points spent to invoke aspects go to the character affected, but only at the end of the scene. And because the GM's NPC pool resets every scene, this effectively means that the GM never gets to put Fate Points in their NPC pool as a result of player invokes.
Richard Bellingham's Fate Point Flow Chart helped me understand where Fate Points go in which situations: https://www.dropbox.com/s/kbi3jrl5kf56ug3/Fate%20Point%20Flow%20Chart.PNG.
It does a useful thing that I think resolves a cloudiness in the Fate Core and FAE rules: it divides the GM's access to Fate Points into 1) an unlimited supply used chiefly for compelling PCs' aspects and awarding points for concessions and 2) the limited NPC pool, which refreshes at the start of every scene and is used by NPCs to invoke aspects.