It does not get rid of Pseudomonas. My pulmo once told me that Pseudo likes to be with other bacterias or some such thing. And if you keep those lower then Pseudo might retreat more. So maybe it helps due to that? Also found this explanation online:

The macrolide antibiotic azithromycin (AZM) provides a paradigmatic example of an “unconventional” antibacterial drug. Besides its growth-inhibiting activity, AZM displays potent anti-inflammatory properties, as well as antivirulence activity on some intrinsically resistant bacteria, such as Pseudomonas aeruginosa.