To my understanding each of those 3 fellowship areas has 3 different requirements to gain rewards. One would expect this is more of a function of the programming and style of event. Changes in 1 shouldn't really impact changes in the other.
Tournament - Complete 1 round of 1 province
Adventure - do anything anywhere on the map, as little as 1 good, 1 relic, 1 badge or 1 orc is enough.
Spire - Based on which gate you get to and if your fellowship has unlocked prizes for that gate. So the minimum here is to reach the first gate assuming fellowship did enough to unlock its prize.