Fury was the only one with a headset.
And yet he seems to talk into the radio regardless.
None of the rest of them ever wear a headset but they still talk as though everyone can hear them...
I thought that was strange in the film as well. I think it was probably an old Star Trek idea that they had the communicators sewed or attached to their clothing or uniforms some how.
Probably Tony's was either in the helmet or IM's suit or maybe in the black clothing he wore underneath.