As far as I understand, auras are available only in alert missions.

But are they supposed to appear also as a pickup object in the middle of the mission, or only obtained as a promised reward after finishing the mission?

2 Answers

Auras can only be obtained from alert missions, when the alert says you will get one. It is given at the end of the mission upon completion. They can not be obtained from any other place, whether mod drop or mission completion.

2

Auras that show up for alert mission are given as an additional reward when you complete the related mission.

This is a guaranteed reward, provided you succeed in doing the mission.