  The standard $\Lambda$CDM model is recently reported to deviate from the
high-redshift Hubble diagram of type Ia supernovae (SNe) and quasars (QSOs) at
$\sim4\sigma$ confidence level. In this work, we combine the PAge approximation
(a nearly model-independent parameterization) and a high-quality QSO sample to
search for the origins of the deviation. By visualizing the $\Lambda$CDM model
and the marginalized $3\sigma$ constraints of SNe+QSOs into PAge space, we
confirm that the SNe+QSOs constraints in both flat and non-flat PAge cases are
in remarkable tension with the standard $\Lambda$CDM cosmology. Next, we
investigate the tension from the perspective of redshift-evolution effects. We
find that the QSO correlation coefficient $\gamma$ calibrated by SNe+low-z QSOs
and SNe+high-z QSOs shows $\sim2.7\sigma$ and $\sim4\sigma$ tensions in flat
and non-flat universes, respectively. The tensions for intrinsic dispersion
$\delta$ between different data sets are found to be $>4\sigma$ in both flat
and non-flat cases. These results indicate that the QSO luminosity correlation
suffers from significant redshift evolution and non-universal intrinsic
dispersion. Using a redshift-dependence correlation to build QSO Hubble diagram
could lead to biases. Thus, the $\sim4\sigma$ deviation from the standard
$\Lambda$CDM probably originates from the redshift-evolution effects and
non-universal dispersion of the QSO luminosity correlation rather than new
physics.
