Until I considered that the 'zero point' between the two dimensions. It's a 'zero point', right? It may be possible that anything originating from that in our dimension could be a complete somwhere else in the other :
I also doubt that the 'zero points' axes are 'aligned' between them... imagine a cloud of striped billiard balls rotating in all directions with no synchronisation at all. All that matters is that the dimension 'sides' are directly opposed to each other.
Antimatter exists and has been produced, and it has been demonstrated that antimatter annihilates matter... but if the above were true, a fermion annihilated in our dimension would also be annihilated in the other. Once the time-space rip maintaining energy is gone, the opposing time-construct will annihilate each other as well.
The above idea is two dimensions that will 'zero out' in all its aspects if all its matter/energy is destroyed, meaning a return to a 'perfect state' nothing, but it is... disturbing, to say the least.