Eldrazi Conscription doesn't actually put counters on anything, just gives a static buff, so it remains unaffected. If the Aura mentioned counters (see Shape of the Wiitigo, for instance), then Doubling Season would affect those.
Doubling Season effects aruas and enchantments. However it only effects counters, not static +x/+x effects. Only cards that use actual counters are effected by doubling season.
Doubling Season