I can understand why it's like that to begin with. Take a look at the '051-Undead01' character sprite. Notice that the yellow dots are the same pattern in every column. Meanwhile, the ghost itself is facing the same direction in each row. This allows you to spin the ghost around while making it play its step animation, preventing the disruption of the animating dots. Essentially, you have two animations play on one character graphic.
In code, the game only resets the walk animation of the character if its new pattern does not match its previous (by pattern I mean what frame of the walk animation you select in the character sprite). In your demo, if you made the second page's graphic be the 2nd (or 3rd or 4th) frame of the walk animation, you will notice that the walk animation stops immediately.
For what you want, you're going to need to do a bit of a trick. On the first page, do a Set Move Route and change the graphic of the event to a different frame than the page's (in case of your demo, anything but the 1st frame). This will trick RMXP into resetting the walk animation so that when you transition to page 2, the step animation will immediately stop.