We employ terahertz Faraday magneto-optical spectroscopy to probe the relaxation dynamics of quantized helical Caroli-de Gennes-Matricon (CdGM) states in epitaxial FeTe₁₋ₓSeₓ thin films, nodeless multiband superconductors with short coherence lengths in the moderately clean limit. By exploiting polarization-selective optical transitions, we directly resolve the helicity and band origin of vortex-core quasiparticles. We observe long-lived CdGM resonances with opposite circular polarizations for electron- and hole-like bands. This enables independent, band-resolved determination of quasiparticle lifetimes, vortex masses, coherence lengths, and upper critical fields, and reveals their systematic evolution with isovalent substitution. The results establish terahertz magneto-optics as a direct probe of helical vortex-core excitations and provide dynamical evidence for multiband CdGM states in iron-based superconductors.