Millimeter emission in photoevaporating disks is determined by early substructures

[abridged]Photoevaporation and dust-trapping are individually considered to be important mechanisms in the evolution and morphology of protoplanetary disks. We studied how the presence of early substructures affects the evolution of the dust distribution and flux in the millimeter continuum of disks that are undergoing photoevaporative dispersal. We also tested if the predicted properties resemble those observed in the population of transition disks. We used the numerical code Dustpy to simulate disk evolution considering gas accretion, dust growth, dust-trapping at substructures, and mass loss due to X-ray and EUV (XEUV) photoevaporation and dust entrainment. Then, we compared how the dust mass and millimeter flux evolve for different disk models. We find that, during photoevaporative dispersal, disks with primordial substructures retain more dust and are brighter in the millimeter continuum than disks without early substructures, regardless of the photoevaporative cavity size. Once the photoevaporative cavity opens, the estimated fluxes for the disk models that are initially structured are comparable to those found in the bright transition disk population ($F_\textrm{mm} > 30\, \textrm{mJy}$), while the disk models that are initially smooth have fluxes comparable to the transition disks from the faint population ($F_\textrm{mm} < 30\, \textrm{mJy}$), suggesting a link between each model and population. Our models indicate that the efficiency of the dust trapping determines the millimeter flux of the disk, while the gas loss due to photoevaporation controls the formation and expansion of a cavity, decoupling the mechanisms responsible for each feature. In consequence, even a planet with a mass comparable to Saturn could trap enough dust to reproduce the millimeter emission of a bright transition disk, while its cavity size is independently driven by photoevaporative dispersal.