Yes new tires do have a break in period where you should drive easy and slower for the first 500 miles of the tires life.
When I had my tires replaced with new tires the tire shop told me that the new tires required a break in period which is to ensure that they deliver their normal ride quality and maximum performance.
The tire shop said to go easy for the first 500 miles of driving on the new tires because some of the lubricant stays on the surface of the tires, and until it completely wears away it can reduce traction.
Not everyone drives easy the first 500 miles and they are okay but if you want maximum performance from the tires and the best traction you should take it easy the first 500 miles.
500 miles seems like a lot of driving but you can easily put 500 miles on the vehicle and tires within a few weeks of driving.