This iPad ad has gotten a lot of notice in classical music circles (which generally like to think of themselves as above crass commercialism while at the same time desperate to find any way to make money).
As an unemployed composer, I don’t begrudge anyone making money of their composing, and Salonen has had an admirable career as both a conductor and composer. While I don’t think he’s the finest contemporary composer, nor in a position to move the tradition into new territories, he produces strong, sometimes excellent music. What you hear in the ad is a fragment of his Violin Concerto, a fine (though not flawless) composition.
The ad does give a look into the compositional process. The conceit that he discovered a tune while whistling as he shaved is best seen as a metaphor, but the the rest is real: coming up with material and working it, working it, working it, until you’ve got something that you can call a composition. For me, the most revealing and true moment is when he’s moving colored post-it notes around a large white board. He’s figuring the best way to make the large-scale structure, and that is not only the essential nuts and bolts of being a composer, but the most difficult part of making any piece with substantial duration.
As for the digital tools he works with, you can see a breakdown with more details and discussion here at the Apple site. He’s using Notion for iPad, and the files he makes he then works with on a computer with the main Notion notation program (I crossgraded to this when the future of Sibelius began to look shaky, and recommend it for all composers—it doesn’t do final engraving as well as Sibelius or Finale, but it is much more useful, and much less confining, for the actual compositional process). When he’s playing a piano keyboard on the iPad, that’s Pianist Pro, which can be used for playing, recording sequences, controller software synthesizers, MIDI, etc., and is a real value. Great for kids to bang away on too.