We investigate the core dynamics behind exotic matter formation via the TQ4Q1.1 set of collinear fragmentation functions for fully charmed or bottomed tetraquarks in three quantum configurations: scalar (0⁺⁺), axial vector (1⁺⁻), and tensor (2⁺⁺). We adopt leading-power single-parton fragmentation within a nonrelativistic QCD framework tailored to tetraquark Fock states. Initial-scale inputs are constructed from updated gluon- and heavy-quark channels, and evolved through threshold-consistent DGLAP within HF-NRevo. We present the first systematic propagation of uncertainties from color-composite long-distance matrix elements governing tetraquark hadronization. This study advances the connection between hadronic structure, precision QCD, and exotic matter.