Tire shops in general are not to be trusted to do a proper job of mounting your tires. If you question a procedure they will inadvertently tell you they have been doing it this way for 20 years. This mean they stopped learning 19 years ago.
1) Pick your tires
2) Be sure to use a dynamic wheel balancing product such as centramatics or counteract balancing beads- very important!
3)When your tire is mounted on the rim have the tech put it on the balancing machine and as it rotates watch the beauty ring so as to be sure tire is mounted true. You should see no eccentric movement at all. If you do see a wobble on the beauty ring have the tech remount it. Check both sides of the tire as it spins for true. Make sure the tech mounts and inflates the tire lying flat on ground, never standing up.
4)While tire is on balance watch to make sure tire is not out of round. you can stand an object such as a hammer close to touching and keep an eye on that. Works well.