Oktas8
The air in the cabin is supporting the weight of the birds which is in turn transferred to the floor of the cabin the same way that a water skier’s weight is supported by the water under the ski which in turn is transferred evenly to the ocean floor.
It all depends on how big the birds are, how many there are and how high they fly in the cabin. Birds flying near the floor would have more of an effect on the CofG than birds flying near the ceiling. As the birds get higher their weight will be more evenly distributed over the cabin as their weight is more evenly distributed across the volume of air in that cabin. If we are only talking about a small number of birds I would say that their weight would be fairly evenly distributed once out of ground effect.

Centaurus

I know the Vampire was subsonic but there still may have been some shock wave on the aircraft, especially since it was over taking you. That would certainly cause an upset if you were close.