pretty sure that it is randomized each scenario. All winning the previous scenario does is allow that player to pick the next one that is played.
No. That's wrong.
Tony is correct.
Basically it's this:
The person who won the previous scenario goes last. So the person after him goes first, then everyone based on the sitting order.
The idea here is that being first gives you advantage (though a minor one*) so if a person one a scenario, he has to go last to slightly balance things out.
* unless playing with pets. At which point, the ability to rush forward and grab a powerful wild one can be huge. I've had scenarios where we caught them on turn 1.