Our early experimental investigation has demonstrated the anomalous surface tension temperature dependence σ(T) at the interface between coexisting liquid-gas phases in magnetic fluids that undergo field-induced first-order phase transition. The σ(T) dependence is anomalous because the drops of a liquid phase condensed under the action of the applied magnetic field H at high temperature T2 exhibit larger surface tension σ(T2) > σ(T1) than the drops condensed at low temperature T1 < T2. This study verifies and confirms the results of the previous experimental investigation of σ(T) in magnetic fluids by performing the experiment, which is based on the analysis of the Plateau-Rayleigh instability of a gas-liquid interface in a zero magnetic field. A novel explanation of this phenomenon is given in the framework of the Stockmayer model. The anomalous increase in σ(T) is explained by the increase in particle concentration difference in gas and liquid phases, which can be attributed to the high field intensity H needed to generate the phase transition at high temperature.