How exactly does the Social Enhancer augmentation work?
The heart/lung/skin temperature monitors are just frill, as far as I can tell - the same animation plays every time they show up.
However, the box at the upper right corner gives extremely useful information as to the target's personality type that will help you decide how to approach the topic, and the persuasion bar in the upper left will show you how effective your tack has been so far.
As for the alpha/beta/omega types, the various personality types react differently to certain kinds of pheromone influence. If you decide to use them, you need to make your choice of which pheromone to use based on which personality type the subject has demonstrated most strongly during the conversation.
The short answer:
Watch the squares. Go with the most squares. Alpha is left, Beta is middle and Omega is the rightmost choice. Many characters flash one alpha square but show the other types longer and stronger, earlier in the conversation.
The long answer:
It seems to be derived from dog training. If I ever do a second playtrough I'll check the game against this theory - I'll try to win the conversations without the CASIE mod. (And help poor Malik this time. ;) ). I agree with Shadur's answer. Except that it also helps to read the psychological fact sheets. It contains hints like: "Can be destabilized by emotional arguments."
According to this theory Alphas are natural charismatic leaders, with natural authority. Like Hugh Darrow and David Sarif. And I guess this politician too. They should be susceptible to real power and strong arguments.
Betas are noisy wannabe leaders. Like the terrorist guy in the first mission. You can bark them into place.
Omegas are the real underdogs. Lowest ranking, lacking in confidence. So according to the theory you can boost their confidence - in the right direction, that is. I'm guessing most scienctists are omega.
It's a funny choice of theory for human interaction. DISC, or MBTI would have been more appropriate.