  We study the fluctuation problems at high temperature in the general mixed
$p$-spin glass models under the weak external field assumption: $h= \rho
N^{-\alpha}, \rho>0, \alpha \in [1/4,\infty]$. By extending the cluster
expansion approach to this generic setting, we convert the fluctuation problem
as a hypergraph counting problem and thus obtain a new multiple-transition
phenomenon. A by-product of our results is a new critical inverse temperature
obtained from optimal second moment estimates. In particular, all our
fluctuation results hold up to the threshold. Combining with multivariate
Stein's method, we also obtain an explicit convergence rate under proper moment
assumptions on the general symmetric disorder. Our results have several further
implications. First, our approach works for both even and odd pure $p$-spin
models. The leading cluster structures in the odd $p$ case are different and
more involved than in the even $p$ case. This combinatorially explains the
folklore that odd $p$-spin is more complicated than even $p$. Second, in the
mixed $p$-spin setting, the cluster structures differ depending on the relation
between the minimum effective even and odd $p$-spins: $p_e$ and $p_o$. As an
example, at $h=0$, there are three sub-regimes: $p_e<p_o, p_o<p_e<2p_o, p_e\ge
2p_o$, wherein the first and third ones, the mixed model behaves essentially
like a pure $p$-spin model, and only in the second regime, it is more like a
mixture. This gives another criterion for classifying mean-field spin glass
models compared to the work of Auffinger and Ben Arous (Ann.~Probab.~41 (2013),
no.~6, 4214--4247), where the idea is based on complexity computations for
spherical models. Third, our framework naturally implies a multi-scale
fluctuation phenomenon conjectured in the work of Bovier and Schertzer (Probab.
Theory Relat. Fields (2024)).
