As someone who USED this reward- yes, it auto-activated, as shown by the timer (personally, I wasted the first 5 minutes trying to get this to work). No, you couldn't use the free stam in regular play. The way it actually worked (for me), you didn't get full stamina for 30 minutes, what happened was you didn't LOSE stamina for fighting- so you still had to wait to earn 2 stam, or pop an item (as I did) to get some stamina to start the fight.
And yes, it was very inconvenient that I couldn't choose when to activate it