that is a common question. simple answer is no.
Tyres have finished offgassing by the time they are used. Even if they hadnt tyres need sunlight and air to offgass.. Tyre walls are entombed with plaster and cannot breath or even have the right conditions to offgass..

also tyre walls dont get hot, since ALL heat is absorbed by the dirt.. Instead they hold a constant temperature.

If you look at a modern home, FULL of toxins from paint, and plastics, there is no comparison!