i no exactly what it is. your tires are 215/40/17 but thats too big for the celica. when your tire is too big, it throws the suspension and steering off. causing your steering wheel to shake at high speeds. i have 215/25/17 on my car and they work great, im pretty sure the size i have on my car is the biggest you can go without messing anything up.
215/40/17 and 215/25/17 are the same size tires
The only difference is your sidewall width is much smaller than his. You got 25, he had 40. Other than that, the tires are the SAME width for the tread. I don't think the sidewall width has much to do with shaking like he has, but it does play a role in handling.