Periodic boundary conditions with vacuum?

Since the ab initio structures are periodic in all 3 directions, do the atoms are the atoms at the bottom of the slab also exposed to the vacuum on the top? To better illustrate my question, here’s an illustration of a catalyst + adsorbate system from the paper:

I drew the main simulation box, everything outside is a periodic image.

Consider the black atom at the bottom - I drew a cutoff radius around it. Since the boundary conditions are periodic, is my understanding correct that this black atom at the bottom of the slab is also exposed to the vacuum?

Correct. Despite periodicity in all 3 directions, the presence of the vacuum effectively prevents the atoms at the bottom of the surface from seeing the adsorbates in the periodic image (as intended).

PS - thanks for the clear illustration!