The bags are tagged priority according to the class of service and whether you are Star Gold or not.

Premiers flying coach don't usually get tags.

Premier Executive and 1Ks get tags regardless of class of service due to being Star Gold.

First/business passengers get tags.

Whether the tags work or not depends on the arrival location. They work better on international flights (Someone mention they store priority bags in a special hold on widebodies).

SFO domestic seems to systematically ignore priority tags. I've had good experiences at SFO international but I do think LAX international is better.