We investigate the influences on the evolution of the Fundamental Metallicity Relation of different selection criteria. We used 5487 star-forming galaxies at a median redshift z~0.63 extracted from the VIMOS Public Extragalactic Redshift Survey (VIPERS) and 143774 comparison galaxies in the local Universe from the GALEX-SDSS-WISE Legacy Catalog. We employed two families of methods: parametric and non-parametric. In the parametric approaches, we compared the Fundamental Metallicity Relation projections plagued by observational biases on differently constructed control samples at various redshifts. Then, the metallicity difference between different redshifts in stellar mass-star formation rate bins. In the non-parametric approach, we related the metallicity and the normalized specific star formation rate (sSFR). To compare galaxies with the same physical properties, we normalized the median of our samples according to the median sSFR at median redshift z~0.09. Then, the galaxies with the same distance from the star-forming main sequence at their respective redshifts are compared when the sSFR is normalized according to the expected values from their respective star-forming main sequence. The methodologies implemented to construct fair, complete samples for studying the mass-metallicity relation and the Fundamental Metallicity Relation produced consistent results showing a small, but still statistically significant evolution of both relations up to z~0.63. In particular, we observed a systematic trend where the median metallicity of the sample at z=0.63 is lower than that of the local sample at the same stellar mass and star formation rate. The average difference in the metallicity of the low and intermediate redshifts is approximately 1.8 times the metallicity standard deviation of the median, of the intermediate redshift sample, in stellar mass-star formation rate bins. We confirmed this result using the Kolmogorov-Smirnov test. When we applied the stellar mass-completeness criterion to catalogs, the metallicity difference in redshifts decreased to approximately 0.96 times the metallicity standard deviation of the median, thus not statistically significant. This result may be dominated by the limited parameter space, being the lower stellar mass galaxies where the difference is larger out from the analysis. A careful reading of the results, and their underlying selection criteria, are crucial in studies of the mass-metallicity and fundamental metallicity relations. When studying the mass-metallicity and fundamental metallicity relations, we recommend using the non-parametric approach providing similar results compared to parametric prescriptions, being easier to use and results fair to interpret. The non-parametric methodology provides a convenient way to compare physical properties, with a smaller impact on observational selection biases.