Priority groups and Session persistence

You are getting confused with 2 different features.

1. PGA (Priority Group Activation) is a feature where you can assign priorities for a set of servers to handle traffic & put logic to goto next set of servers when a min required servers are not present.

    

2. Session Persistence : This holds your user preferences like username & pwds.

    

So its obvious when you apply persistence, it will not time out immediately.