Problem with variables

I had trouble downloading your file. However, based on your description, I'd say the problem is the "when" of your trigger. If it's set to run when the timeline starts, then the trigger checks the value of the variable before the user can hover over the tiles. 

Here's what you could do instead: Use 4 triggers. Each would change Next to Normal when one of the variables changes, with the conditions that all the variables are True. 

By the way, you might want to reconsider hovering vs clicking. Anyone using a mobile device can't hover, so they'd be unable to advance. If you require clicking instead, and give each tile a Visited state, you'd just need one trigger to change Next to Normal when all 4 tiles are Visited.