  Recently an `outliers' track of radio-X-ray correlation was found, which is
much steeper than the former universal correlation, where dual tracks were
speculated to be triggered by different accretion processes. In this work, we
test this issue by exploring hard X-ray spectral evolution in four black-hole
X-ray binaries (XRBs) with multiple, quasi-simultaneous radio and X-ray
observations. Firstly, we find that hard X-ray photon indices, $\Gamma$, are
anti- and positively correlated to X-ray fluxes when the X-ray flux, $F_{\rm
3-9keV}$, is below and above a critical flux, $F_{\rm X,crit}$, which are
consistent with prediction of advection dominated accretion flow (ADAF) and
disk-corona model respectively. Secondly and most importantly, we find that the
radio-X-ray correlations are also clearly different when the X-ray fluxes are
higher and lower than the critical flux that defined by X-ray spectral
evolution. The data points with $F_{\rm 3-9keV}\gtrsim F_{\rm X,crit}$ have a
steeper radio-X-ray correlation ($F_{\rm X}\propto F_{\rm R}^{b}$ and $b\sim
1.1-1.4$), which roughly form the `outliers' track. However, the data points
with anti-correlation of $\Gamma-F_{\rm 3-9keV}$ either stay in the universal
track with $b\sim0.61$ or stay in transition track (from the universal to
`outliers' tracks or vice versa). Therefore, our results support that the
universal and `outliers' tracks of radio-X-ray correlations are regulated by
radiatively inefficient and radiatively efficient accretion model respectively.
