Tubular tires have a few differences with clincher tires. One of them is that tubulars automatically take much longer to cure than clinchers do.

Whenever a tire is made there is solvents used in the rubber to liquify it. The solvents need to evaporate out for the rubber to achieve its full strength.

With a clincher tire, the solvents can dissipate out either direction (through the exterior [tread] side or through the interior side of the tire) and then they blow away. So clinchers can be manufactured very quickly, especially if volatile solvents are used that can be driven out quickly with heat.

With a tubular tire, the solvents that evaporate out to the inside end up trapped in the tire, until they can work their way out again, completely through the entire thickness of the tire. So a tubular would need at least 3 times as long to cure than a clincher the same thickness, and might need much longer.

Being tubulars also explains why they can be stored safely in piles like shown in that video: there is enough air trapped in each tire to make sure that it maintains its round cross-section. If you sucked all the air out of them and left them sit crushed flat for a few years, they'd all be cracked where the casings had been folded.