  The spatial decorrelation of dense molecular gas and young stars observed on
$\lesssim 1$ kiloparsec scales in nearby galaxies indicates rapid dispersal of
star-forming regions by stellar feedback. We explore the sensitivity of this
decorrelation to different processes controlling the structure of the
interstellar medium, the abundance of molecular gas, star formation, and
feedback in a suite of simulations of an isolated dwarf galaxy with structural
properties similar to NGC300 that self-consistently model radiative transfer
and molecular chemistry. Our fiducial simulation reproduces the magnitude of
decorrelation and its scale dependence measured in NGC300, and we show that
this agreement is due to different aspects of feedback, including H$_2$
dissociation, gas heating by the locally variable UV field, early mechanical
feedback, and supernovae. In particular, early radiative and mechanical
feedback affect the correlation on $\lesssim 100$ pc scales, while supernovae
play a significant role on $\gtrsim 100$ pc scales. The correlation is also
sensitive to the choice of the local star formation efficiency per freefall
time, $\epsilon_{\rm ff}$, which provides a strong observational constraint on
$\epsilon_{\rm ff}$ when the global star formation rate is independent of its
value. Finally, we explicitly show that the degree of correlation between the
peaks of molecular gas and star formation density is directly related to the
distribution of the lifetimes of star-forming regions.
