We investigated the population of low-mass central galaxies with M∗ = 109.5-1010 h-1 M⊙, inhabiting regions near massive groups and clusters of galaxies using the IllustrisTNG300 and MDPL2-SAG simulations. We set out to study their evolutionary histories, aiming to find hints about the large-scale conformity signal they produce. We also used a control sample of central galaxies with the same stellar mass range located far away from massive structures. For both samples, we find a subpopulation of galaxies accreted by another halo in the past, but now considered central galaxies; we refer to these objects as former satellites. The number of former satellites is higher for quenched central galaxies near massive systems, with fractions of 45% and 17% in Illustris TNG300 and MDPL2-SAG, respectively. The differences in the numerical resolution of each simulation lead to the different fractions of former satellites. Our results in TNG300 show that former satellites "pollute"the sample of central galaxies because they suffered environmental processes when they were satellites hosted typically by massive dark matter halos (M200 ≥ 1013 h-1 M⊙) since z ≲ 0.5. After removing former satellites, the evolutionary trends for quenched central galaxies near massive structures are fairly similar to those of the quenched control galaxies, showing small differences at low redshift. For MDPL2-SAG instead, former satellites were hosted by less massive halos, with a mean halo mass around 1011.4 h-1 M⊙, and the evolutionary trends remain equal before and after removing former satellite galaxies. We also measured the two-halo conformity, that is, the correlation in the specific star formation rate between lowmass central galaxies and their neighbors at megaparsec scales, and how former satellites contribute to the signal at three different redshifts: z = 0, 0.3, and 1. The time evolution of the conformity signal in the simulations presents apparent contradictory results: it decreases from z = 0 to z = 1 in MDPL2-SAG, while it increases in TNG300. However, after removing former satellites in the latter, the signal is strongly reduced, but practically does not change at z = 0.3, and it disappears at z = 1. We compare our findings with recent literature data and discuss the conformity measurements, as different approaches can lead to varying results.