Cosmic voids, the largest underdense regions in the Universe, provide unique laboratories for studying galaxy formation and constitute powerful probes of cosmology. Recent work has shown that individual galaxy bias (b_i), which quantifies how each galaxy traces the underlying dark matter field, exhibits a characteristic radial dependence within spherical voids, defining a void bias profile in which galaxies near void centers display systematically lower bias values. We investigate how the environmental modulation of individual galaxy bias depends on the adopted void-finding algorithm by comparing measurements across five distinct void definitions: spherical voids 'sparkling', watershed-based methods ('zobov' and 'revolver' in two modes), and free-form integrated-density voids ('popcorn'). We apply these complementary void-finding algorithms to the same galaxy sample drawn from the IllustrisTNG simulation (TNG300-1 at $z=0$) and compute individual galaxy bias profiles as a function of distance from void centers. We quantify the correlation between b_i and the membership of the void catalogs and explore how this relationship varies with the integrated underdensity threshold for density-based methods. We find that the radial gradient of individual bias within voids, generally increasing from negative values at the void centers to higher values at the boundaries, is robust across most void definitions. However, density-threshold methods preferentially select galaxies with b_i<0, while watershed methods without density constraints include substantial contamination from high-bias boundary galaxies. The correlation between negative bias and void membership is systematically strengthened as the integrated underdensity threshold becomes less restrictive, with popcorn achieving the highest purity in isolating anti-biased populations.