When is the Richest Settler evaluated?
The latest core Settlers of Catan (link to PDF) rules state:


  If you have 10 or more victory points during your turn the game ends and you are the  winner! If you reach 10 points when it is not your turn, the game continues until any player (including you) has 10 points on his turn.


And the Traders and Barbarians (link to PDF) scenarios state:


  The normal rules for The Settlers of Catan apply. The changes are described below.


Therefore, we can infer that the rules for determining the winner apply here too, and while the amount of victory points required may change, when the winner is calculated is unaffected.

Even though Player 2 will have more victory points, it is NOT their turn, so Player 1 will win as soon as he/she has the necessary points.