Consider the diagram below of two detectors-emitters exchanging photons: Thin lines are null-paths between detectors. Detectors are also synchronized in such a way that measurements outside the blue or red windows are ignored. So first detector can only react to photons received in the red window, and the 2nd detector can only react to photons on the blue window.
First detector has some amplitude $\psi_A$ to emit photon from some point $A$ inside the apparatus red window, and second detector has some amplitude $\phi_C$ to emit photon from inside blue window. The key assumption here is that that second apparatus is made such that amplitude $\phi_C$ depends on a photon having being received at some point $B$ inside the measurement blue window. So $\phi_C(B)$ actually depends on past local events in the apparatus.
Now, while the observables and correlators for photons separated by space-like paths like $A-B$ or $C-D$ must commute, Feynmann propagators only vanish exponentially inside the space-like separations, and presumably a measurement of photons at some point $D$ inside the red measurement window of detector 1 are not restricted by space-like commutator rules, presumably the correlations between observations $A$ and $D$ do not need to be zero
Question: Can we expect the correlators between $A$ and $D$ events be zero, or just exponentially small in proportion to the length of the red and blue reaction windows (and their separation from the lightcones)?