I think you pretty much have it. The imagery intended is that of the mythical bird. Wiki has its contribution here:
http://en.wikipedia.org/wiki/Phoenix_(mythology)
Ryo Noda is well known (to saxists) as a composer of many of these types of unaccompanied works, which you probably know. Improvisations I-III, Mai, Fantaisie et Danse are others. He studied with Hemke and Londeix. Also at least worked (maybe lived) in Toronto, Canada.
The piece contains his trademark use of many interesting sounds and techniques which may include quarter tones, multiphonics, alternate timbre fingerings, growling etc.
It was a great piece to hear -- I actually saw it performed with an interpretive dancer. Sounds a bit cheesy but it was a neat visual spectacle.