Jack shoots Garibaldi as the Chief is on his way to warn Sinclair and possibly the President of what is about to happen. Once he's down, Garibaldi ceases to be an immediate threat. It is possible, even probable, that the conspirators on the station have other work to do in support of the plot, and don't have time to trouble themselves with Garibaldi. They leave him to die where he lays.
Later, after the President is dead, Jack learns that Garibaldi has made it to MedLab and may be able to talk. At this point it becomes necessary to kill Devereaux and his thugs, who would not otherwise have been connected with Garibaldi's shooting.
I'm not sure why everybody assumes that Devereaux and his men are carrying unregistered PPGs at that point, by the way, or even assuming that the gun Jack "finds" on Devereaux's body is actually his. According to Jack's account only Devereaux pulls a gun on him. He fires in self-defense and presumably shoots the other two in the act reaching for something - a justifiable shooting under the circumstances. It isn't certain that they were even armed. Certainly Jack would want to point suspicion away from the intelligence services, however, so he'd be much smarter to plant stolen, traceable, PPGs on the mens' bodies. Surely such things are not hard for a security officer to come across in downbelow. I'm sure Jack realized what a mistake it was for Devereaux to have an untraceable weapon on him when Garibaldi took him in earlier. Why compound that error? Instead he gets his fellow security officers to join him in covering up his execution of the three men responsible for wounding their chief, perhaps mortally, and no one suspects a thing. With Devereaux and company dead, and the assassination designed to look like an accident (as Jack surely knew it would be) there is no trail to follow. And he'll be doing the investigation himself anyway, whether or not Garibaldi gets past the immediate crisis.
Regards,
Joe