The β decays of the ground state (gs) and isomeric state (m) of 96Y have been studied with the total absorption γ-ray spectroscopy technique at the Ion Guide Isotope Separator On-Line facility. The separation of the 8+ isomeric state from the 0− ground state was achieved thanks to the purification capabilities of the JYFLTRAP double Penning trap system. The β-intensity distributions of both decays have been independently determined. In the analyses the deexcitation of the 1581.6 keV level in 96Zr, in which conversion electron emission competes with pair production, has been carefully considered and found to have significant impact on the β-detector efficiency, influencing the β-intensity distribution obtained. Our results for 96gsY (0−) confirm the large ground state to ground state β-intensity probability, although a slightly larger value than reported in previous studies was obtained, amounting to 96.6+0.3−2.1% of the total β intensity. Given that the decay of 96gsY is the second most important contributor to the reactor antineutrino spectrum between 5 and 7 MeV, the impact of the present results on reactor antineutrino summation calculations has been evaluated. In the decay of 96mY (8+), previously undetected β intensity in transitions to states above 6 MeV has been observed. This shows the importance of total absorption γ-ray spectroscopy measurements of β decays with highly fragmented deexcitation patterns. 96mY (8+) is a major contributor to reactor decay heat in uranium-plutonium and thorium-uranium fuels around 10 s after fission pulses, and the newly measured average β and γ energies differ significantly from the previous values in evaluated databases. The discrepancy is far above the previously quoted uncertainties. Finally, we also report on the successful implementation of an innovative total absorption γ-ray spectroscopy analysis of the module-multiplicity gated spectra, as a first proof of principle to distinguish between decaying states with very different spin-parity values.