Original cap rubbers don't have a thin or thick part.
They are both the same.
The correct way has to be the way the rubber fills out the space from the edge to the inner upstanding middle part.
So there should not be space left.
I think with your seal the thin part goes up.
This part was made thin to make it easier to put the seal on without taking the whole cap appart.
In the factory they put on the seal and than pressed the cap together. (Zink part in the chrome cover).