  Chern insulators are topologically non-trivial states of matter characterized
by incompressible bulk and chiral edge states. Incorporating topological Chern
bands with strong electronic correlations provides a versatile playground for
studying emergent quantum phenomena. In this study, we resolve the correlated
Chern insulators (CCIs) in magic-angle twisted bilayer graphene (MATBG) through
Rydberg exciton sensing spectroscopy, and unveil their direct link with the
zero-field cascade features in the electronic compressibility. The
compressibility minima in the cascade are found to deviate substantially from
nearby integer fillings (by $\Delta\nu$) and coincide with the onsets of CCIs
in doping densities, yielding a quasi-universal relation
$B_c$=$\Phi_0\Delta\nu/C$ (onset magnetic field $B_c$, magnetic flux quantum
$\Phi_0$ and Chern number $C$). We suggest these onsets lie on the intersection
where the integer filling of localized "f-orbitals" and Chern bands are
simultaneously reached. Our findings update the field-dependent phase diagram
of MATBG and directly support the topological heavy fermion model.
