Being who he was, and more importantly, what he used to be Alaster did indeed listen to the owner's speech. While he had no idea what she was talking about when it came to calling the sentient home a TARDIS, he did understand the concept of what she was. He was after all a very old man, relatively speaking.
Alaster, again being the man that he was took upon himself to introduce himself, seeing as the owner had so graciously done the same. Alaster was nothing without his manners. "Thank you miss for the lovely introduction." Alaster said as he ran his fingers through his hair once more. "My name is Alaster MorningStar." he said without being prompted "And it seems that I owe your lovely friend Rose a thank you." Alaster said as he bowed his head in thanks. "I found myself in a rather nasty pickle only a few moments ago." he added.
"I too come from Earth, although I would wager that it is an alternate version of yours." he said as he pointed on lazy, clawed finer at the owner. "The year was 1940 and I called Los Angeles home. Until events there forced me to leave rather quickly." At that Alaster grew silent once more.