=/ I'm sure i'd mentioned that was going to be the case, and it really shouldn't be hard for you to see why, and what you need to do to have the animation play on selection.
There's a state called "remove item from pattern". which transitions to "is pattern complete". instead have it transition to a duplicate copy of the "Show Item", "Bool Test" and "Small Pause states" and link "Small Pause 2" to "is pattern complete".
Now, after this, you're going to come back to me and say "But now i have to wait for the animation to finish playing before I can select the next one". Yes. If you don't want this, you need to remove the Bool Test 2 State you've created, so it doesn't need the animation to finish playing before allowing input.
"But now I can't click the cubes quickly because it's under the floor during it's animation" - Yup. Seperate the mesh and collider into 2 objects, so you can move the button's mesh, without moving the collider you need to test against.
As you can see, you can keep coming back with more and more issues... At this point I think it's fair to say your original question has finally been answered!
you've got a working example of how to animate your cubes properly. I don't have the time to guide you through every step of your game development. Take some time playing around with the system you've got now to try and implement the things you want. The best way to learn is experimentation, not from being given step by step guides.
You'll still find the help you need on these forums, when you run into an issue you can't solve... Just give things a try first =)