No, when you add him to the party, turn on self switch B.
You've got a page conditioned by B, followed by a page that does nothing but turn B on. That's not right.
What's happening is that it's looking at your event pages from the last to the first, and as soon as it finds one whose conditions are met (page 4) it makes it active.
There are a few things wrong with your events. First - I don't see where you actually add the new player to your party. When you've done what he asked you to do and he joins the party, you need to have a Change Party Members: Add Mark command so he actually JOINS the party. THERE is where you need to turn on self switch B. Then get rid of tab 4 altogether.
Now, apparently you have to kill 10 rats, and when he asks you, you say you've killed them all, but your conditional branch only checks to see if ONE has been killed. So if you only kill 1 and leave the other 9, this will still happen ... unless you have a troop of 10 rats. But that's a different matter.