Both prepositions 'upon' and 'on' are correct in this sentence. The difference there is that 'upon' has a more formal tone and usage than 'on'.
The difference between 'as soon as' and 'upon/on' is the perceived time. 'As soon as' makes it sound like "she said...." Happened immediately after. It sounds more directly connected to her receiving the prize. 'Upon/on' also indicate that what "she said" happened very soon after, but perhaps not as direct and connected as 'as soon as'.
If you want to emphasise how fast she said what she said, 'as soon as' is your best choice.
If you don't need to emphasise that quickness, but just a sequence of events, use 'upon' or 'on'.