Okay, I've been popping them every time I play only to get one exotic for the four hours it last. What give???? Please tell me i'm not the only one.....
Placebo effect at it's finest. Pretty sure a number of sources have experimented with the Fireteam Medallions and haven't found a noticeable increase in the number of rewards received or an increase in the quality of rewards given. Without a clearly defined percentage or value associated with the increase, you're better off to just continue playing as regular without them.
Slightly better rng is still rng.