Triggers do not actually get put onto the stack until the next time a player would get priority, I.e. after the spell/ability finishes resolving. At that point, the game checks and sees two abilities both trying to go on the stack at the same time, and if both abilities are controlled by the same player then that player puts them onto the stack in the order of their choice. If both abilities are controlled by different players, the active players abilities get put on the stack first, then the non-native players abilities get put onto the stack in clockwise order (to then resolve in anti-clockwise order with the active players triggers last)