  The ringdown data of both GW150914 and GW190521\_074359 (GW190521r) show
evidence supporting the presence of overtone. Previous studies all adopt a
fundamental assumption, which were motivated more by convenience than by first
principles, that the first overtone and the fundamental mode share a same
onset. In this work, for the first time we relax such assumption, and we aim to
probe the possible chromatic onsets of these two components within the GW150914
and GW190521r ringdown data. For both events, we bound the onset lags to be
$\Delta t_0\geq 5M_f$ at probabilities of $\geq 94.7\%$, where $M_f$ is the
mass of the remnant black hole formed in the merger. This result moderately
favours the non-simultaneous excitation between the fundamental mode and the
first overtone in the ringdown.
