This work certainly is not "authentically Spanish", nor was it ever meant to be taken as such. But the three movements were inspired by traditional dances and structured in Classical forms: Habanera/Sonata, Pavane/Variations, Bolero/Rondo (with themes borrowed from the first two movements).
I have written several brass works undertitled Parodie, based either on existing music or, as in the present case, on familiar musical styles, often with ethnic or national references. I use the term parodie in its medieval sense and without satiric intent. -Stanley Friedman, 2003, Memphis, TN, USA