It depends on the tire construction. I can only tell you about tires I've used on my db30. It originally came with p330 tread 145/70-6 made by Wanda Tyre Ltd from China. Wanda P330s are sold as directional and they expect you to have them spinning in the direction of the center arrow on the tread face as there is no spin direction listed on the sidewall. I've cut these tires apart when they are taken off my mini and I've noticed that the nylon belts are spun leaning towards the direction of the rubber arrows on the tread face. That means the they are molded with the strength from the center hub twisting out towards the spin direction of the "arrows" on the tread face. I used them for asphalt stree and grass on my DB30 with a slightly worked 212 and was happy with the results. The frame of a DB30 puts a shitload of stress on the back tire because it carries the most weight, has all the thrust torque, and all the braking is done there so the rear tire takes the most punishment. I am going to switch the rear tire to a Wanda P333 (sometimes they are sold as Wanda/Journey or simply Journey tires with the Wanda logo on them) which is a symettrical square pattern across the whole face of the tire since the only thing my DB30 will see is asphalt and grass.
These tires also have no sidewall directional arrows, so when I cut one open i expect to see the nylon belts wound from the center bead to the road face of the tire in a straight crosshair pattern.
In my humble opinon, since I've had this DB30 well up over 60 mph, the biggest issue for me is balance. I can feel and have to counter steer the wobble because of how difficult it is to get one of these small tires reasonably balanced on a low speed rim. The tires are not designed for high speed applications (rubber distribution is not quality controlled as meticulously) and the rims are not much better. Its very difficult to spin balance one of these small tires on a small rim unless you have all day to do it. I have pics of my chewed up p330 wandas on my db30 for you to see. Short answer is the tread direction probably plays a key part in how the tire was molded.
Here's what im using now for street and grass only. Wanda P330s.
Notice the rear tire is chewed up from the sidewall on up. Thats damage from the asphalt street from turning and acceleration.