Actually the bottom 400 FO, a July 18 hire, is HSV based. The last 400 class is currently half ANC, a third LAX and a couple each HSV and CVG.
Atlas's home reserve (R1) is more meant to have crewmembers ready to airline out somewhere than cover a flight departing from their base airport. It's a way to have you on the schedule when Scheduling hasn't figured out what to do with you. It's unpaid and the time spent on R1 doesn't count towards your rig. The response time depends what time the company calls. If contacted between 7 and 12 local you have to be able to depart in 5 hours. If they call between 12:01 and 6:59 you have 10 hours to depart.