Selected State Won't "Stick"

Jesse is correct about the Hover state overriding the Selected state. However, eliminating the triggers won't solve the problem. That's because Hover and Selected (and Visited) are built-in states. They come with automatic functionality. 

• When an item has a Hover state, that state will automatically display when the user’s mouse is over the item. The Hover state will go away when the user’s mouse is no longer over the item.
• When an item has a Visited state, that state will automatically display when the user clicks the item.
• When an item has a Selected state, the first click automatically changes the state to Selected. The next click changes it back to Normal. And repeated clicking toggles between the two states.
• When multiple items with the Selected state are in a button set, clicking one of those items will change it to Selected and will automatically change the other items in the set to Normal. (Here’s more information: https://community.articulate.com/series/articulate-storyline-360/articles/articulate-storyline-360-user-guide-how-to-work-with-button-sets.)
• Here's more info about built-in states: PRIMER: Take advantage of built-in states | Articulate - Community 

Using triggers that duplicate built-in functions can actually cause problems. So all the triggers that change to built-in states should be deleted. 

Personally, I'm not a fan of the Hover state. I'd delete it. However, if you want to keep it, I suggest that you make the Hover state look like the Selected state (that is, with the colorful fill) with the addition of the glow. 

By the way, all of the items in the button set should have a Selected state. Your "correct" item has a Visited state but not a Selected state. When it changes to Visited after being clicked, it will stay in that state. So you'll need to delete the Visited state and use a Selected state instead.

Your Hover states keep overriding your Selected and Visited states.

Disable all Hover triggers and try if that is what you want.