There's good reason why rubber tires are not allowed in landfills. The rubber contains toxic chemicals which leach into ground water. Ground/chipped tires contain zinc (causing Zn phytotoxicity) , cadmium, arsenic, lead, nickel, and other heavy metals. All dangerous for sensitive wildlife. In a confined space, such as a mews, the odor itself would be overwhelming. It's marketed for landscaping because it KILLS plants (weeds, etc.). It is NOT recommended for food-producing gardens. Imagine rubber chips sticking to your bird's food and being ingested. I would recommend against using this material anywhere around your bird or its mews.
P.S. My grandchildren aren't allowed to play in playgrounds having rubber mulch either.