Variables & triggers

You wrote: "When clicked, each one shows a layer for a short time, then shows a "visited" state." - but that's not actually how it works. The 'visited' state is a built-in state that automatically changes to visited the second the button is clicked - not after it does whatever trigger you have on it (like view a layer). When they select the fourth icon, it will instantly change to visited, which should trigger both the 4th layer AND the Webpage layer to open. 

If the layer properties on all layers are set to 'hide other layers' you'd only see whichever one happened to open last (triggers that theoretically run at the same time (like on click or timeline start) don't happen simultaneously; they happen one after another, fractions of a second apart, in order listed in the triggers panel). My guess is that the trigger to open the fourth layer is further down the list than your trigger to show layer webpage.

If want to manually trigger the icon to change states after the layer is viewed 'for a short time', then you could duplicate the visited state of the icons but name it something like 'viewed' (something other than a reserved state that has built-in behavior already attached to it, like 'visited'). Then trigger the icons manually to change to 'viewed' when desired (vs when clicked), and update the trigger to show layer Webpage when the state of all of the icons is 'viewed'