Hi All,
The one and biggest factor for the band to"feel good about you", is to show sincere interest in them.
Ask them about their genre, and how they see themselves down the track, what direction they want to take the music.
Most bands who are taking on new members, (drummers) use this opportunity to bring a fresh element into their music, just to break the "routine grind"
THIS is where You come in!
Ask them to play a part of one of their most favorite songs, and do not drum with them straight away.
Ask them what kind of feel they are looking for, with regards to rhythm.
THEN drum say, 16 bars, with them after which you ask, "Is this sort of what you are after?"
My experience is that they (like many people) love to be talking about them selves, so let them.

As the most inportant ingredient of making music is communication, you will do well to make it easy for them.
I started to have more (a lot of) success with auditions when I adviced afterwards that they should get more drummers in to compare, so they were getting a better idea which one could fit the band best.
I got this advice from a very wise friend, by giving the signal that you want them to get the best for the band (unselfishly) you will get the job, providing that you are an OK drummer though! Also, that way you do not seem to be desperate, and they will have the feel that also YOU have other options.
They rather setlle for a communcative OK drummer than for an arrogant brilliant one!
And also, bring good gear, (you can always borrow for the time being, ha-ha),
and be on time, and ONLY give a Solo when they ask for it!
Cheers and Happy Drumming,
Harry