When Tom Paris is in astrometrics lab, one of the screens has a colorized image of the Helix Nebula. This nebula is actually in the Alpha Quadrant.
As Voyager fires on Alice, the Doctor informs the Captain that she must stop because they are disrupting Tom's neural pathways. At this time, they had not made any sort of connection to Tom or Alice. There is no way for the Doctor to have that detail of information just from scanning a shielded ship.
It is uncertain what Alice means when she describes the particle fountain as "home," since she is nothing more than a computer program.