I am so happy you asked this question, @Lydswatch! And I’m glad the question was regarding the timer. I use that most often, too.
It seems the top, right button turns on whichever app is first. I tested that theory by moving other apps to that first place. Pressing the top, right button turns that app on.
Edit to include another wonderful surprise: You can also customize the bottom, right button! Move the desired app (in my case, Weather) so that it sits right below the first app. That app now gets opened easily by pressing the bottom, right button. See below.