Do try a bi-exponential fit with
f(t) = A\cdot e^{-t/\tau_1}+B\cdot e^{-t/\tau_2}
I’m sure there’s some literature around for fitting multiple exponentials for CRDS signals and why that might make sense.
Looks to me like an exponentially clamped oscillation, like a damped harmonic oscillator.
Possible, but I doubt it. The apparent oscillation is a typical artifact when fitting a bi-exponential signal with a single exponential.