I didn’t have any screen changing on my head unit. I will bring up a notification on any screen that I have a new target coming with the distance counting down.
But unlike a planned outside workout, every new target doesn’t create a new lap. So in order for me to have a useful lap (interval) power I have to manually hit the lap button.
The only page that gets automatically switched to on my wahoo is strava live segments. That will change the screen when a starred segment approaches. But never had this experience with Best Bike Split.
One thing to note is that when I run it as a simulation on my Kickr, I get the target power field but not the notifications on any screen. I assume they think that indoors you will be looking more closely at the head unit and not require notifications.