I've thought of a new way of phrasing my question that may help clear up some confusion:
Do states store all of the information about what they display, or only the parts that are different from the Normal state?
The first option would mean that when an object is in its Visited state, Storyline only displays the Visited state.
The second option would mean that when the object is in its Visited state, Storyline displays the Normal state and then applies the changes for the Visited state (in my example, it would change the font and fill colours).
I really appreciate your offer to help though. I've attached a story file with just the button in question. Following your advice, I recreated it from scratch (without the text boxes for each state), taking extra care to only edit the properties of each state that I wanted to apply when combined. However, the same thing happened as before, and only one state applies at a time.