The HADS system takes advantage of both the TARDIS’ clairvoyance and its ability to travel in time by dematerialising shortly before an attack takes place. It’s a highly effective system and that’s been a problem for Time Lords in the past (or future) who’ve left the system on, left their TARDIS and then watched it dematerialise without them as soon as they get in trouble. The system on the Justice Station lacks this problem due to the fact the crew rarely, if ever, leave.