First, let's recapitulate what we know. Both phases have different densities, one that is lighter is always on top. However, solution density changes with the solute concentration - see
density tables for examples. When both phases have similar density at the beginning of the extraction it may happen that when solute moves from one phase to the second, density of both phases changes - and phase that was lighter now becomes heavier. That's when the density inversion may happen.
In your case concentration of solute is so small (1mg/1mL, about 0.1%) that you may safely assume no density changes at all. Water at the bottom, ethyl acetate on top. Check density tables on the page I have posted - note that for 1% solutions density changes rarely reach 1%.
Water phase is often acidified or basified when the substance is a weak acid or weak base, to move dissociation equilibrium as far to the left as possible. For example weak acid in acidified solution gets protonated, thus it is mostly in non-ionic form - which is soluble in non-polar solvent like ethyl acetate. That helps in extraction. It may be also used other way around - if you want to get as much of the acid from the non-polar phase, you will use basified water, to neutralize acid.
That being said, I have no idea why this particular solution is acidified - dibenzothiophene doesn't look like an acid to me...