Yeah, exactly what he said. You can also hold down the right bumper, and select any of these "commands" from a list of them. In almost all instances, it places an icon above your head to let your squadmates know you need a health pack or ammo or a ride somewhere. It's a fantastic system, really, for when your squadmates are in a closed party or just not on chat.
As far as using the headset, I'm not exactly sure, but I am reasonably certain if you have the headset plugged in, the actual microphone in the Kinect is deactivated. I left my headset plugged in one night, and it was the only time I've had any really trouble with Kinect recognizing my commands, so I assumed it was because the headset microphone wasn't good enough to accurately hear me from across the room.