LU: as Avram in MD wrote, it depends on the person. There is no consensus on whether the arm with the tefillin is put in the jacket sleeve or not. It all depends on the person’s comfort. If my jacket sleeve is big enough, I will put my hand into the jacket sleeve. If not, I leave it out.
The covering of the arm tefillin is based on the words UKKSHARTEM LOS AL YADCHAH (tied as a sign on your hand) as a reminder to the wearer not to the observer.