Quantum error correction can preserve quantum information in the presence of local errors; however, errors that are correlated across a qubit array are fatal. For superconducting qubits,high-energy particle impacts due to background radioactivity or cosmic ray muons produce bursts of energetic phonons that travel throughout the substrate and create excitations out of the superconducting ground state, known as quasiparticles, which poison all qubits on the chip. Here we use thick normal metal reservoirs on the back side of the chip to promote rapid downconversion of phonons to sufficiently low energies where they can no longer poison qubits. We introduce a pump-probe scheme involving controlled injection of pair-breaking phonons into the qubit chips. We examine quasiparticle poisoning on chips with and without backside metallization and demonstrate a reduction in the flux of pair-breaking phonons by more than a factor of 20. In addition, we use a Ramsey interferometer scheme to simultaneously monitor quasiparticle parity on three qubits for each chip and observe a two-order of magnitude reduction in correlated poisoning due to ambient radiation. Our approach reduces correlated errors due to background radiation below the level necessary for fault-tolerant operation of a multiqubit array.