You might find out the newly obtained puppy was chasing the cat being surrendered
whenever he would go by the litter box, or the episodes of urinating outside of the litter box took place only after the cat returned from
outdoor adventures, or the cat would soil in the hallway right outside of the laundry room where the litter box was kept (could the soiling be related to the cat being scared by the sound of the washer and dryer?).