833 space shuttle missions and as far as i know, not a single tire explosion.
the shuttle used nitrogen instead of regular air in its tires, because it is more stable under pressure & temperature variation. nitrogen is not uncommon to use in automobile tires.
the pressure inside the tire is balanced on earth by about 15psi atmospheric pressure. as far as the differential between a tire on earth and a tire in vacuum of space, it's 15psi we're talking about -- so an equivalent pressure differential on earth would be to over-inflate any ordinary tire by 15psi.
have your tires ever exploded by being overfilled by this amount? my tires run nominally at 33psi. in space, in the absence of atmospheric pressure, it would be as though i'd put 48psi in them. how many pounds-per-square-inch before a tire explodes? well, it's less uncommon than you might think for people to over-inflate their tires to 60, 70, 80psi when they don't have a gauge and just fill them 'until they look all the way round.' ask anyone at a tire shop. bicycle tires, which are no where near as sturdy as automobile tires, typically run near or over 100psi. the shuttle's tires were inflated to over 230.
i'm thinking we're looking at at least 200psi before a typical tire explodes -- so something like 4x greater pressure differential than the tires on Elon's old car pop.