We report that at ambient temperature and with 100% enriched para-hydrogen (p-H-2) dissolved in organic solvents, paramagnetic spin catalysis of para -> ortho hydrogen conversion is accompanied at the onset by a negative ortho-hydrogen (o-H-2) proton NMR signal. This novel finding indicates an electron spin polarization transfer, and we show here that this can only occur if the H-2 molecule is dissociated upon its transient adsorption by the paramagnetic catalyst. Following desorption, o-H-2 is created until the thermodynamic equilibrium is reached. A simple theory confirms that in the presence of a static magnetic field, the hyperfine coupling between unpaired electrons and nuclear spins is responsible for the observed polarization transfer. Owing to the negative electron gyromagnetic ratio, this explains the experimental results and ascertains an as yet unexplored mechanism for para -> ortho conversion. Finally, we show that the recovery of o-H-2 magnetization toward equilibrium can be simply modeled, leading to the para -> ortho conversion rate.