  $R^2$-corrected dark energy (DE) models in $F(R)$ gravity have been widely
investigated in recent years, which not only removes the weak singularity
potentially present in DE models but also provide us with a unified picture of
the cosmic history, including the inflationary and DE epochs. Towards the
unified interpretation of dynamical DE all over the cosmic history in the class
of $R^2$-corrected DE models, we explore the universal features of the scalaron
dynamics in the radiation-dominated epoch, along with the chameleon mechanism,
by keeping our eyes on the inflationary and DE epochs. We show that the
scalaron evolution does not follow a \textit{surfing solution} and is mostly
adiabatic before big bang nucleosynthesis (BBN), even properly including the
\textit{kick} by the nonperturbative QCD phase transition, hence a catastrophic
consequence claimed in the literature is not applied to this class of DE
models. This is due to the presence of the gigantic scale hierarchy between
$R^2$ correction and DE, so is the universal feature for the class of
$R^2$-corrected DE models. The prospects for the post- or onset-inflationary
epoch would be pretty different from what the standard $R^2$ inflationary
scenario undergoes due to the presence of the chameleon mechanism.
