PSIONIC CONSTRUCTS: Terrain markers placed by Bunker are not removed until they are destroyed or until Bunker uses a power that places that type of terrain marker on the map.

Say he has a barrier up, do the old barrier tokens disappear when he is given an action to use barrier or do they remove after he uses barrier?

As soon as you give an action to place those tokens again. So they will be removed before you place new ones.