Predetermined, but random. I have kept track of what the success of the different Saints are for Dawn, since I use her to build up the other heroes, and the success is not always the same. I do not know about stars, since I do not do stars on Dawn before the transfer to the other hero.
I suppose that we could all share out experiences on how many medals it tool to get each star and see if it is always the same. In any case once the random value is determine, it does not change, and that is what it makes it look as it is predetermined.
There is one thing that is not predetermined, at least not 100%, and that is what you get from a Guild Chest. The kind of item you get (like leve 1 chip, purple hero, etc) is predetermined, but the specific one is not. If you are going to get a purple hero, for example, you can 'X' out of the card flop screen and open the chest again until you get the one that you want.