The Tier ranking is an industry supply relationship. It has nothing to do with quality/lack of quality other than the perception by the consumer that the corporate brand used that supplier so the tire must be the best for that use.
Tier one tire companies are those that supply tires to vehicle manufacturers.
Tier two tire companies supply tires to the vehicle manufacturers and the consumer aftermarket.
Tier three tire companies supply tires to the top tier tire brands and to independent brands. They may also sell their own brand.
Using this tier definition, a Pirelli or Dunlop tire may not qualify as a tier one tire but a Falken or Hankook may. To further muddy the water, even folks in the industry use the tier rankings as a perception of quality, i.e. "Oh, that Bridgestone is a Tier One tire, it's better than a Yokohama" when that might not be the case. Also, a vehicle Mfg. may have a relationship with a tire manufacturer that makes their tire brand a Tier one tire. Ford had just such a relationship with Firestone prior to 2000.
"Fuzzy" as Capri Racer notes, is entirely correct.