Alpha, Beta and Omega refer to personality types. The social enhancer influences these types in different ways, and you have to choose the right personality type when you activate the augmentation.
When you are having a conversation with someone where the social enhancer can be used, the game will bring up a cue telling you to press a button to release pheromones. Once you do this, you will be given three options. You can Appease the person, Charm them or Pressure them. Each option corresponds to one personality type, Alpha, Beta or Omega. Choosing the right one unlocks the reward. You have to pay attention when the conversation is happening to see which personality spikes the highest, as the will often display more than one type. You need at least 2 bars to be able to make a choice, though sometimes 2 personality types will spike to 2 and you need to a level 3 spike.
If you want more information, this web site is detailed and lists the effects of successfully using the enhancer:
http://deusex.wikia.com/wiki/Social_Enhancer