When I tween move the camera between objects, more often than not, the css3d object that is in front of the camera disappears when the tween starts or ends.
The problem might be related to your camera animations. Right now you call moveCameraToProject() on each click which means you perform multiple tweens at the same time. Maybe you can avoid the mentioned problem by removing the previous camera animations in order to ensure only one active camera tween at any time. This is also done in the following example:
I think it’s best if you try to isolate the problem in a small live example. Besides, a fiddle makes it easier to debug the code and verify possible solutions.