Hi Mark,
vehicle manufacturers do not hold stock of third party supply items, production lines are designed to run on bare minimum of parts on the shop floor (Often close to Zero at the end of a shift)
the Master Production Schedule dictates what is required and when, it’s not unusual for suppliers to make several deliveries per day under Just in Time policy / contract.
for example VW do not supply a spare tyre as standard, so for example you order a spare tyre & all weather option, it is perfectly feasible that your van is the only van to be produced, that day, that requires 5 all weather tyres, fitted to 4 alloys and one steel wheel ! (unlikely but entirely possible) VW will not want spare tyres / wheels kicking around on the production line.
VW will not care what make the tyre is and will schedule delivery to suit themselves based on the contractual agreement with the various suppliers (I.e. minimum volume vs min cost)