dynamics of the electrons and holes changes the local offset-charge environment for qubits near the impact site. The phonons that are produced have energy above the superconducting gap in the films that compose the qubits, leading to quasiparticle excitations above the superconducting ground state when the phonons impinge on the qubit electrodes. An elevated density of quasiparticles degrades qubit coherence, leading to errors in qubit arrays. Because these pair-breaking phonons spread throughout much of the chip, the errors can be correlated across a large portion of the array, posing a significant challenge for quantum error correction. In order to study the dynamics of γ-ray impacts on superconducting qubit arrays, we use a γ-ray source outside the dilution refrigerator to controllably irradiate our devices. By using charge-sensitive transmon qubits, we can measure both the offset-charge shifts and quasiparticle poisoning due to the γ irradiation at different doses. We study correlations between offset-charge shifts and quasiparticle poisoning for different qubits in the array and compare this with numerical modeling of charge and phonon dynamics following a γ-ray impact. We thus characterize the poisoning footprint of these impacts and quantify the performance of structures for mitigating phonon-mediated quasiparticle poisoning.