The excited states of unstable \(^{20}\)O were investigated via \(\gamma\)-ray spectroscopy following the \(^{19}\)O\((d,p)^{20}\)O reaction at 8 \(A\)MeV. By exploiting the Doppler Shift Attenuation Method, the lifetime of the 2\(^+_2\) and 3\(^+_1\) states were firmly established. From the \(\gamma\)-ray branching and E2/M1 mixing ratios for transitions deexciting the 2\(^+_2\) and 3\(^+_1\) states, the B(E2) and B(M1) were determined. Various chiral effective field theory Hamiltonians, describing the nuclear properties beyond ground states, along with a standard USDB interaction, were compared with the experimentally obtained data. Such a comparison for a large set of \(\gamma\)-ray transition probabilities with the valence space in medium similarity renormalization group ab-initio calculations was performed for the first time in a nucleus far from stability. It was shown that the ab-initio approaches using chiral EFT forces are challenged by detailed high-precision spectroscopic properties of nuclei. The reduced transition probabilities were found to be a very constraining test of the performance of the ab-initio models.