True diamond tufting is a lost art. And I've done plenty of it in furniture upholstery on antiques using horse hair or palm fiber and cotton. All done by hand. Early auto upholstery was more similar to furniture upholstery, but that all changed as time advanced. Almost all upholstery was covered in muslin first back in the day. The tuck and roll sewn panels would be upholstered over a muslin base. Pretty simple, coil springs, hand tied together. Covered in burlap then horse or hog hair then covered in cotton. A muslin cover held it all in place. Then the final upholstery. Can't say for sure, but foam probably came around in the early 60's in new cars. This all happened when flat "S" no-sag springs replaced coils. Foam was thicker and could make up the height that was lost when tall, coil springs went away. Coil springs would last for decades, foam not so much. Foam has its place in modern auto upholstery for sure, but it doesn't hold a candle to the durability of coil springs and cotton. Repair and reuse your old seat springs whenever possible. There are a bunch of ways to do pleats, channels, tuck and roll.... Anything you wanna call it. But these days it will most likely be done with foam and last only as long as the foam does.
A really interesting discussion and I do love T and R upholstery. But, when it came time to do the door panels of my A coupe, which are the only real parts you can see (the seats are leather covered Fiero's), I went with what a '60s rodder might do and used a machine pleated vinyl, similar to what was available then from JC Whitney. It was around a lot when I was a kid. I think it looks great, it was relatively quick and inexpensive and it is period correct. But, it's not tuck and roll.
Read this, it is close but doesn't use cotton or hair. http://www.hotrodders.com/forum/tuck-roll-tutorial-146204.html
He got the sewing method correct, but the outcome with the flat foam looks like ****! Look at the flat "rolls" and wide "tucks" , it's really the lazy man's method. Real tuck and roll is labor intensive, and the effect is achieved with lots of work. Flat pleats to me are just too common and just tell me he took the easy road..... From the article you sent: