  The segregation of oxygen in the high critical temperature cuprate
superconductor $La_2CuO_{4+y}$ has been systematically studied along the years.
In a recent set of experiments, Poccia et al related, for the first time, time
ordering ($t$) of oxygen interstitials with the corresponding superconducting
transition temperature $T_c(t)$. We develop a phenomenological description of
the time ordering forming pattern domains and show how it may affect the
superconducting interaction. The superconducting self-consistent calculations
in a system with electronic granular structure of varying hole doping yields
also different local d-wave amplitudes. These amplitudes are of the order of
magnitude of scanning tunneling microscopy measurements and they vanish at
$T^*(t)> T_c(t)$. Then, calculations with Josephson coupling among the isolated
charge domains reveal that the superconducting interaction is likely to be
scaled by the local free energy and capture the details of $T_c(t)$. The
accurately reproduction of these apparently disconnected phenomena establishes
routes to the important physical mechanisms involved in the connection between
sample production and on the origin of the superconductivity of cuprates.
