Abstract There has been an upsurge of interest in two-nucleon decays thanks to the studies of nucleon–nucleon correlations. In our previous work (2021 Phys. Rev. Lett. 126 142501), based on a novel time-dependent three-body approach, we demonstrated that the energy and angular correlations of the emitted nucleons can shed light on the structure of nucleonic pairs formed inside the nucleus. In this work, we apply the new framework to study the decay dynamics and properties of some extreme proton-rich and neutron-rich oxygen isotopes, including two-proton (2p) decays of ^11,12O and two-neutron (2n) decay of ²⁶O. Here we show that the low-ℓ components of ^11,12O wave functions, which are affected by continuum and configuration-interaction effects, strongly impact decay dynamics and asymptotic correlations. In the calculated wave functions of ^11,12O, diproton and cigarlike structures merge together during the tunneling process and the resulting energy and angular correlations are very consistent with the experimental data. The asymptotic correlations of the 2n decay of ²⁶O dramatically change as the 2n decay energy approaches the zero-energy threshold. The small reported value of Q _2n suggests that the 2n decay of this nucleus can be understood in terms of the universal phase-space limit.