Yeah, I thought you might. But my reading is supported by the text here (see highlight):
View attachment 152583
If you stop the XP the moment a PC reaches XP for the next level, such as in your example of stopping the Thief at 1251 XP for level 2, they would not have added the qualifier "OR GREATER THAN", which indicates it is certainly possible to earn XP sufficient to gain more than one level. Once the adventure is done and the DM calculates XP and awards it,
then you cannot earn more until you train. You cannot, once XP is awarded, go back out (prior to training) to earn more XP for the sake of convenience to train for two levels at once.