It's like the French "voici" as opposed to "ici."
Why not "Тут ваш десерт."?
Not a Ukrainian speaker, but my understanding is that тут is for the relative location "here" and ось is for when you're presenting or pointing something out.
That's what it seems like to me too. Would be nice if someone else could confirm this.
In British English dessert and pudding are interchangeable