The role of the interaction with the nearest electronic state \(^3\Sigma^+_{0^-}\) on the hyperfine structure and magnetic properties of the \(a(1)[^3\Sigma^+_1]\) state of PbO is assessed. The accounting for this contribution leads to difference between \(g\)-factors of the \(J=1\) \(\Omega\)-doublet levels, \( \Delta g = 37\times10^{-4}\), that is in a good agreement with the experimental datum \( \Delta g = 30(8)\times10^{-4}\). The contribution of this interaction rapidly grows with \(J\). For \(J=30\) the difference of \(g\)-factors of \(\Omega\)-doublet states reaches 100%; for hyperfine constants it is 18%. These differences also depend on the electric field and for \(E=11\) V/cm for \(^{207}\)PbO the difference in \(g\)-factors turn to zero. The latter is important for suppressing systematic effects in the electron electric dipole moment search experiment.